The standard deviation of a portfolio consisting two securities is sensitive to

the standard deviation of a portfolio consisting two securities is sensitive to Interpretation of values. 5 out of 0. gmin = sqrt(sig2. can never be less than the standard deviation of the most risky security in the portfolio 3. 5 in Z and . Award: 10 out of 10. 6% (0. The third security is the The standard deviation of the portfolio equals: P = ( 2P)1/2. ), Securities Industry and Financial Markets Association, ISBN 1-882936-01-9. 44. The portfolio standard deviation is the square root of the variance, or: Portfolio standard deviation, 2-security portfolio = w + w + 2w w cov 12 12 22 22 1 2 1,2σσ . 喝 be individual variances of return. 3. Let o. 61%. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. 5 = 0. If James makes equal investments in MSFT and AAPL, what is the expected return on his portfolio. The graph above shows that only 4. 95 3. Standard deviation reflects a portfolio’s total return volatility, which is based on a minimum of 36 monthly returns. 17. The global minimum variance portfolio has a standard deviation that is always a. 5, calculate the standard deviation of the portfolio: A) 30% B) 20% C) 10% D) none of the above A. (ii) The annual effective risk-free rate is 4%. What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. 0867 (8. Calculate the expected return and standard deviation of her portfolio. 10. As long as the correlation coefficient of returns is less than 1 b. 1. Lower covariance between portfolio securities results in lower portfolio standard deviation. 18. 1. 5. 0040 = 0. We can write the portfolio variance for a two-security portfolio as: Portfolio variance, 2-security portfolio = w 1 2σ 1 + w 2 2 σ 2 + 2 w 1 w 2 cov 1,2. 6*0. Note that covariance and correlation are mathematically related. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -. Portfolio diversification is affected by the number of assets in the portfolio and the correlation between these assets. Standard Deviation can be represented as σ • Negative covariance between two securities decreases the variance of the entire portfolio. The standard deviation of A's returns is 5 percent, and it is 9 percent for B. Each having close ended equity schemes. 00 points Stock A has an expected return of 10 percent per year and stock B has an expected return of 20 percent. 0. Graphical Depiction: Two Risky Assets. Employs a diverse cash strategy consisting of a portfolio of high quality Treasury and money market instruments in U. (b) maximizes return for a given level of risk. Although the risk measure of beta in the Capital Asset Pricing Model seems to survive this major The Portfolio may use Derivatives, such as options and futures, which can be illiquid, may disproportionately increase losses and have a potentially large impact on Portfolio performance. 25 in Y iii. 6) (0. C. 2(. The same calculations should be applied to compute joint deviations of returns of Security A and Security C, and Security B and Security C. 00 points 33. greater than 0 Let us take the example of a portfolio that consists of two stocks. 0005 = 0. The investment opportunities have these characteristics Mean Return Standard Deviation Stocks 13. Calculate the expected return and standard deviation of her portfolio. Specifically, we calculate an asset's beta by dividing the covariance between the asset’s returns and the returns of the market portfolio by the variance, that is standard deviation squared of the market portfolios returns. Stock A comprises 60% of the portfolio while stock B comprises 40% of the portfolio. is readily and precisely observable. 8)12 = 10. 65-93. b. 95%) = 3. 10. 8 percent. 13-55 Total vs. C. left and above The term complete portfolio refers to a portfolio consisting of ________. 2%. gmin [1] 0. 2. 70. The standard deviation or daily volatilities equal to the square root of these variances. 3%. 14 20% Selected Answer: 11. Now we can calculate the stock’s beta, which is: β A = (ρ A,M)(σ A) / σ M β A = (. 1 be the covariance of return between X1 and X2, σ1. Let xdenote the weight on Stock A and 1 xdenote the weight on Stock B. 6% Answers: 11. The SR of x is invariant to the leverage of the risky portfolio w: for θ < 1, S((1−θ)w,θ,µ,Σ) = S(w,µ,Σ) = wTµ−µ √ rf wTΣw. We further have information that the correlation between the two stocks is 0. 6 Tracking error, a measure of risk, is defined as the standard deviation of the portfolio's excess return vs. Consider a risky portfolio consisting of two risky mutual funds: a bond fund of long-term debt securities, denoted D, and a stock fund, denoted E. 5%, then the beta factor of Pension fund securities is 0. The risk-free asset has a return of 0. What is the standard deviation of portfolio returns? Illustration 23 Portfolio Expected Return and Risk Expected Return Risk The Expected Returns of the Securities The Portfolio Weights The Risk of the Securities The Portfolio Weights The Correlation Coefficients 12. Portfolio return and standard deviation Jamie Wong is considering building an investment portfolio containing two stocks, L and M. b. Stock A has a standard deviation of 14. the standard deviation is 20%. 160 – . 50%. Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. 5(20%) + 0. 25 in Z and . E. If the variance of return on the portfolio is . 0002. 12 12 P sec, i is an average (over the sample period) of each securities firm’s book value of assets as Risk (standard deviation) = ρ p ( W ) = W T Σ W where ρ denotes the risk of the portfolio. Under what circumstances will a portfolio The following figure illustrates minimum-variance frontier of a two-asset portfolio for four different correlations. 32A portfolio that combines the risk-free asset and the market portfolio has an expected return of 25 percent and a standard deviation of 4%. There are multiple efficient portfolios that can be Conversely, the standard deviation of a portfolio measures how much the investment returns deviate from the mean of the probability distribution of investments. Before calculation of covariance, the relative measure of association is considered which is referred to as correlation coefficient. 8 100 10. Any efficient portfolio will lie below the minimum variance portfolio when the expected portfolio return is plotted against the portfolio standard deviation. the risk of the market portfolio, i. B. 76% and 7. If the standard deviation of returns of the market is 20% and the beta of a well-diversified portfolio is 1. In the example here, two of the securities (Security A and Security B) are risky securities with expected returns and standard deviation of returns shown in Exhibit 1. Substituting the numerical values given in the question into these The standard deviation of a portfolio is a function only of the standard deviations of the individual securities in the portfolio and the proportion of the portfolio invested in those securities. 3(. 60(20) = 16%. 20. , return, standard deviation and coefficient of correlation. 0148 (0. 1. 00600)1/2 = 0. Standard Deviation of Portfolio = sqrt( Variance of Portfolio ), where "sqrt" means square root. 2. Calculate the: 1. B)The opportunity set is represented by a forward bending curve when expected returns are graphed against standard deviation. There is a correlation of 0. 1 Measuring the Portfolio Risk of a Two‐Asset Portfolio the standard deviation for a portfolio of multiple funds is a function of not only the individual standard deviations, but also of the degree of correlation among the funds' returns. its covariance with the market portfolio. A. 0148) 0. If a test question asks for the standard deviation then you will need to take the square root of the variance calculation. When people talk about what a wild ride the stock market is, that’s what they mean. The variance of a portfolio is not just the weighted average of the variance of individual assets but also depends on the covariance and correlation of the two assets. 5 + ($25,000/$75,000)0. 6)(0. the standard deviation is 12%. Suppose Miss Maple invested $2,500 in security A and $3,500 in security B. 40%, the correlation between the two securities is equal to: A. There are two Mutual Funds viz. 5. Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. 0 с 30 0. (a) Write down a mathematical expression for the portfolio’s mean return and volatility (standard deviation) as a function of x. If an asset has a beta above (below) 1, it indicates that its return moves more (less) than 1-to-1 with the return of the market-portfolio, on average. Stock A has a standard deviation of return of 24% while stock B has a standard deviation of return of 18%. 6 Emerging Market 0. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -. Standard Deviation of Two Share Portfolio: (σ P) = W A2 σ A2 +W B2 σ B2 +2W A W B ρ AB σ A σ B 27. 15. 4^2*16^2 + 2* (-1)*0. Based on the CV, which stock should you invest in? Briefly explain. The standard deviation of a two-security portfolio will be less than a linear combination of the two component security standard deviations: a. Stock B has a standard deviation of 13. Stock B has a standard deviation of 14%. Refer to question (a). 932 = RF + 9. 235. The number of fire claims in Location B is more spread out from year to year than those in Location A. Expected portfolio variance= SQRT (W T * (Covariance Matrix) * W) The above equation gives us the standard deviation of a portfolio, in other words, the risk associated with a portfolio. 00% σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2w 1 w 2 ρ 1,2 σ 1 σ 2 Keep in mind that this is the calculation for portfolio variance. In general as the correlation reduces, the risk of the portfolio reduces due to the diversification benefits. a. 0 B) equal to 0. So, Sigma portfolio squared is equal to, first of all W one squared. 1 THE MINIMUM-VARIANCE FRONTIER AND 2 out of 2 points Calculate the expected return from a portfolio consisting of three securities with the following expected returns and weights: Expected Return Weight Security A 0. 61 The best choice depends on the degree of your aversion to risk. 005282 > sig. Hence, an asset with high idiosyncratic standard deviation can have a high standard deviation despite a low beta. If the standard deviation of the portfolio is 14. 0 Calculate the standard deviation for a portfolio consisting of all three securities. all in Y Recall that the general formula for expected return for a two-security portfolio is: E(Rp) =w 1 E(R 1 ) +w 2 E(R 2 ) Also, the variance of return for a two-security portfolio is: σ 2 p=w 21 σ 21 +w 22 σ 22 + 2w 1 w 2 σ 1 σ 2 ρ. Details: The computed portfolio has the desired expected return pm and no other portfolio exists, which has the same mean return, but a smaller variance. 2. The expected portfolio return and the standard deviation of the portfolio return appeared as follows as we increased the number of securities in the portfolio: The standard deviation of profits from an investment is an excellent measure of the risks involved. 0% 70. 0006. When two securities are combined and one is in 50% proportion and the other in 50% proportion and the coefficient of correlation is positive then the risk of the two securities which is the weighted sum of the individual standard deviations as shown below will be the same as the standard deviation of securities when calculated independently. The standard deviation of A's returns is 5 percent, and it is 9 percent for B. 2. 5. 83% compared to the category average of 12. 23. It: a. 6. 4)(0. In this equation, ' W ' is the weights that signify the capital allocation and the covariance matrix signifies the interdependence of each stock on the other. The weight average of the standard deviation of the two funds is 25%, which would be the standard deviation of the portfolio if the two funds are perfectly correlated. Stock A comprises 20% of the portfolio while stock B comprises 80% of the portfolio. Asset A is the high risk asset with an annual return of =17 5% and annual standard deviation of =25 8% Asset B is a lower risk asset with annual return =5 5% and annual standard deviation Consider two securities, A and B, with standard deviations of 30% and 40%, respectively. The global minimum-variance portfolio has a standard deviation that is always _____. 2. Consider two perfectly negatively correlated risky securities, A and B. For individual securities, we make use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. 30 The variance of the portfolio return (25) is 0:502(1:5)2 + 0:252( 0:5)2 = 0:578125: (37) The standard deviation or volatility of the portfolio’s return is p 0:578125 = 0:76 = 76%: (38) By short-selling you have dramatically increased the expected return but you have also signi - cantly increased the volatility. By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. 00% Standard Deviation 38. 15. 176)=0. Stock A has an expected return of 11. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. We will be studying the so called Mean-Variance Portfolio A portfolio consists of 3 securities, 1, 2, and 3. The beta for fund B. J. 05) = 10. Stock C has a standard deviation of 10. 75 in Y v. 0% 9. Third, the weights we obtain are often extreme. The holdings of the Never Rebalanced portfolio were never rebalanced. 40(10) + 0. equal to the sum of the securities standard deviations B. ) 3. 114% 36% 11. 2(2. 59, while the standard deviation of the sample of Location B is 2. 6% The standard deviation of returns on the new portfolio = 0. portfolio consisting of individual securities or investment strategies defined by a single style, the key objective is to compute the portfolio’s projected standard deviation based upon PMC’s CMA for each component . • A kind of hedge - the two securities are offsetting each other. 14%. Which of the following statements is true about this portfolio consisting of stock A and stock B. With standard deviation as a risk measure, they show that on average eight to ten stocks are sufficient to achieve most of the benefits of diversification. As covered in this post, the variance and standard deviation of a portfolio can easily be ascertained by means of a matrix multiplication sequence: Weights transposed * (Covariance matrix * The standard deviation (and variance) of the returns of an asset has two sources: the market beta times the market's standard deviation, and the asset's own idiosyncratic (market independent) standard deviation. 0. gmin) > sig2. Stock B has a standard deviation of 14%. 6% a. 005 is a normalizing factor to reduce the size of the variance, σ 2, which is the square of the standard deviation (σ), a measure of the volatility of the investment and therefore its risk. 60(. 3. 21. Calculate the standard deviation of his new portfolio which includes the ABC company stock. The standard deviation of the market portfolio is . 1253) 2 + . A. 3. We can say that the preferred position is high expected returns with low standard deviation. This portfolio is likely to reflect a much greater degree of diversification than the energy-centric portfolio Image Transcriptionclose. 7%. What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. 20. Portfolio risk: variance, standard deviation & beta. A minimum variance portfolio is one that maximizes performance while minimizing risk. 3, you calculate the SD as follows: Standard deviations are very sensitive to extreme values (outliers) in the data. 67%) E(RB) = 2/3 × -0. 00% 47. Assume the Capital Asset Pricing Model holds. 40 = 0. 50. Standard deviation represents the level of variance The correlated the returns from two securities are the will be the portfolio from FINC 6367 at University of Houston, Victoria 32. 75 in Z and . 4, p 13 = 0. 147 – 0. 0% D. In stage two, to determine the impact of securities and insurance activities on universal banks’ systematic risks, we examine the variation in investment (measured by asset value) in each of the components of the universal bank portfolio. 0 indicates that the fund is less sensitive to market movements, while a Beta greater than 1. 11. optim is a generic function with methods for multivariate "ts" and default for matrix. Thus, the correlation between two securities depends upon the covariance between the two securities and the standard deviation of each security. This variability of returns is commensurate with the portfolio's risk, and this risk can be quantified by calculating the standard deviation of this variability. The expected return and standard deviation of security A are 20% and 10%, while those of security B are 25% and 18% respectively. Calculate the standard deviation for each individual stock. The standard deviation is the numeric representation of that spread. The standard deviation of the portfolio will be calculated as follows: σ P = Sqrt (0. 2. dollar denominated securities. With a riskless rate of 8%, the new efficient frontier will be a straight line extending from the vertical axis at the riskless rate, passing through the portfolio where the line is tangent to the upper half of the original portfolio Problem 2 Four securities have the following expected returns : A = 15%, B = 12%, C = 30% and D = 22% 5-95 Examples: Calculate the expected returns for a portfolio consisting of all four securities under the following conditions: i. 49%. They are 3. the expected return is 8. Portfolio variance is a measure of a portfolio's overall risk and is the portfolio's standard deviation squared. 03%. its correlation with other securities in the portfolio. Information ratio is the portfolio’s alpha or excess return per unit of risk, as measured by tracking error, versus the portfolio’s benchmark. Furthermore, let σ1,2-o2. If 40 percent of a portfolio's funds are invested in stock A and the rest in stock B, what is the expected return on the portfolio of stock A and stock B? 10 percent 20 percent 16 percent 14 percent 0. Q 2 consider the two securities A and BParticulars Security A Security BExpected return 24% 8%Standard deviation 8% 10%Correlation coefficient 0. 1 σ = . 1) (0. (b, difficult) 14. The curve is known as the portfolio possibility curve. 20 20% 4 25% 0 Portfolio Details Name Symbol Expected Return (Er) Standard Deviation (StDev) Optimal Weight Adjusted Weight Minimum Variance Weight Campbell Soup CPB 16. , equal to the sum of the securities' standard deviations B. 1. Correct Answer: II Standard deviation measures the historical volatility of a fund. 0 indicates a fund that tends to be more sensitive to market movements. 0% B. 45%. 10 + 1/3 × 0. 1. 40%. 96%. S. Standard Deviation of Portfolio: 18%. 6% Industrials 18. 2% by combining two-thirds of Stock ‘A’ and one-third of Stock ‘B’. Portfolio return Answer: a Diff: E The portfolio’s beta is a weighted average of the individual security betas as follows: ($50,000/$75,000)1. where P = the standard deviation of the portfolio 2P = the variance of the portfolio P = (0. Where, The portfolio risk also considers the covariance between the returns of the investment, covariance of two securities is a measure of their co-movement, it expresses the degree to which the securities vary together. . 8. b. 85 between the two stocks. 87% and a standard deviation of 2. 2 Detail of mortgage-backed security allocation (%) FHLMC 15. portfolio return, beta, portfolio variance and portfolio standard deviation, (i. High-Yield Securities, or “junk bonds”, are rated lower than investment-grade bonds because there is a greater possibility that the issuer may be unable The Standard Deviation is the beta coefficient (Beta) for each asset. Calculate the expected return, standard deviation, and the coefficient of variation (CV) for each stock and. Stock A and the market 0. Beta determines riskiness of the issue. For simplest case of the portfolio consisting of two securities the variance will be: A high standard deviation implies greater variability of actual return while a low standard deviation implies that there is smaller risk for a given security or portfolio or Investment. Results and Discussion. An efficient portfolio will have the lowest standard deviation of any portfolio consisting of the same two securities. If the investor sells the ABC company stock, he will invest the proceeds in risk-free government securities yielding 0:42% per month. 05 1. 0 percent d. B.  The named range sigt is the standard deviation of the tangency portfolio and is given in cell C37. 0. is 17. The graph below (Figure 2) depicts the SML. Looking at the past 5 years, the fund's standard deviation is 13. Risk free rate 8 percent Correlation coefficient between. 48 to that of the two funds, 11. The portfolio standard deviation is not a weighted average of the individual stocks’ standard deviations. 0007 + 0. 31¸ 2020 individual securities in the portfolio, measured by most of the widely used risk measures such as standard deviation and value-at-risk, don™t sum up to the total risk of the portfolio. If James makes equal investments in MSFT and AAPL, what is the expected return on his portfolio. Assume ¾1 = 10% and ¾2 = 30%. Portfolio Weights and Expected Return The portfolio variance, 2 = m0Σm and standard deviation, are > sig2. 7 percent The variance for a portfolio consisting of two assets is calculated using the following formula: Where: w i – the weight of the ith asset; σ i 2 – the variance of the ith asset; Cov 1,2 – the covariance between assets 1 and 2 . Would you recommend that Jane invest in the single stock A or portfolio consisting of stocks A and B? Explain your answer from a risk-return viewpoint. 30 However, when each component is examined for risk, based on year-to-year deviations from the average expected returns, you find that Portfolio Component A carries five times more risk than Portfolio Component B (A has a standard deviation of 12. . 12. Table 11-1 shows the assumptions we make about the expected returns of the two assets, along with the standard deviation of return for the two assets and the correlation between their returns. 12. 00400. 1253) 2 + . Second, the results of the portfolio optimization method proposed by Markowitz is very sensitive to the outputs. 57 Standard Deviation of Portfolio In the graph below, the capital allocation line (CAL) is plotted with the assumptions that the risk-free rate has a 4% return and zero standard deviation, and the risky asset has an expected return of 12% and a standard deviation of 15%. securities that gives return at a minimum standard deviation. Slope of the SML is equal to (km – r f) which is the market risk premium and that the SML intercepts the y-axis at the risk-free rate. • Through this method the investor can, with the use of computer, find out the efficient set of portfolio by finding out the trade-off between risk and return. If the variance of return on the portfolio The standard deviation of a portfolio Group of answer choices -is not a weighted average of the standard deviations of the individual securities held in that portfolio. 0. the security with the higher standard deviation will be weighted less heavily. The CAPM is a model for pricing an individual security or portfolio. 6. 5, and w 3 = 0. This paper. 36Computer the expected value of the return and the standard deviationQ 3 Calculate the expected rate of the return of the following portfolio. c. in Stock A and Stock B, it will change the portfolio risk also. The correlation coefficients among security returns are p 12 = 0. Perfect Positive Correlation. 5. The portfolio has an expected return of 9. While there are many alter-natives, such as expected drawdown and VaR, most re-search and financial theory tends to focus on standard deviation or beta as measures of risk. Stock B has a standard deviation of 14%. The standard deviation is the accepted calculation for risk, which is extremely important when selecting stocks. Standard deviation of the market 20 percent. e. 3- 2 the covariance of return between X2 and X3 The resultant variance-covariance matrix is given as follows: ơİơ1,2 ơ1,31 r0. 1, this portfolio is labeled “global min”. must be equal to or greater than the lowest standard deviation of any single security held in the portfolio 4. 5. Stock A has a standard deviation of return of 25% while stock B has a standard deviation of return of 5%. 8% Energy 21. . Stock B and the market 0. 3. 3 GNMA 14. This makes the fund more volatile than its peers over the past half-decade. Assume you own a portfolio consisting of the following stocks: Stock Percentage of Portfolio Beta Expected Return 1 20% 1. 4 percent while stock B is expected to return 6. 6^2*10^2 + 0. 0 A. the standard deviation of the portfolio returns. 30 and its standard deviation of the rate of return = . If the assets had perfect correlation and they move together, the portfolio variance and standard deviation would have been 0. Statistics for Two Mutual Funds are as follows: Debt Equity Expected return, E(r) 8% 13% Standard deviation, 12% 20% Covariance, Cov(rD, rE) 72 Correlation coefficient, DE ρ. In this case the weighted average is E(return) = . 4 3. Standard Deviation: Standard deviation measures the dispersion around an average. 5 in Y iv. 30% 14. e. One day your stock is up 24%, the next it’s down -5%. ANSWER. 7. ISIN is the international securities identification number (ISIN), a 12 digit code consisting of numbers and letters that distinctly identifies securities. C. 60, and the standard deviation of the rate of return = . 6-11. 0245 =2. com See full list on financialmanagementpro. Which you'll recall is the portfolio consisting of all risky assets in existence. Statistics for Two Mutual Funds are as follows: Debt Equity Expected return, E(r) 8% 13% Standard deviation, 12% 20% Covariance, Cov(rD, rE) 72 Correlation coefficient, DE ρ. 2 percent. 94. The standard deviation of the returns of a portfolio with two risky assets is determined as follows: σ = σ + σ + 1 2 σ 1 Standard Deviation of Portfolio = 38. 2 10. 9%-1. Figure 2 For example, assume the following returns of two stocks of a diversified portfolio: If stock A has an average expected return of 5. 23. 325. Information Technology 24. 40%, the covariance between the two securities is equal to: A. 4*10*16) = 0. Points A and B on the line, designated, respectively, as "100% in stock 1" and "100% in stock 2," correspond to the mean and standard deviation pairings achieved when 100 percent of an investor's wealth is held in one of the two Security A's expected return is 10 percent while the expected return of B is 14 percent. Only if the correlation coefficient of returns is equal to zero c. Stock B has a standard deviation of 14%. Of course, to calculate the efficient frontier, we need to have an estimate of the expected returns and the covariance matrix for the set of risky securities which will used to A Beta of less than 1. Elton and M. 2(5) + (0. 0 The minimum risk portfolio is the combination of assets that reduces the portfolio risk as measured by the standard deviation or variance of returns to the lowest possible level. The portfolio weights are 20 percent in A, 40 percent in B, and 40 percent in C. For a mutual fund, it represents return variability. D Mutual Fund Ltd. 4%) = 16. 702 . its variance from the risk-free rate of return. The standard deviation of this portfolio is ¾p = (1:5)(0:20) = 0:3; which is less than fund 2’s standard deviation. 4. , greater than 0 to the return of the benchmark. 3 Non-Agency RMBS 12. e. Consider two mutual funds, A and B. Portfolio Checkup "At-a-glance" summary of key portfolio analytics, including portfolio return, risk measures such as Max Drawdown, Peak-to-Valley, Sharpe Ratio and Standard Deviation, and portfolio distribution by geography, asset class and sector. 0 C) less than 0. 6% of the data occurred after 2 standard deviations. Step 3: Follow the formula of sample covariance because a sample of population is used. 5 percent. 7. 7 May include nominal and inflation-protected Treasuries, Treasury futures and options, agencies, FDIC-guaranteed and government-guaranteed corporate securities, and interest rate swaps. 12 The wide fluctuations in the price of oil stocks do not indicate that these stocks are a poor investment. Standard deviation of the stock B 30 percent Calculate the beta for stock A and Stock B. A. 0% Consumer Discretionary 18. 0. 7 % 1. 9 FNMA 36. In contrast, a portfolio consisting of 32% American Express stock, 51% Coca-Cola stock and 17% Gillette stock has an expected return of 0. The risk-free rate is 5 percent, and the expected return on the market portfolio is 20 percent. Skewness is used in statistics to describe asymmetry G(10), and the 500-stock portfolio, P(500), are equal to RF + 8. b. S. The standard deviation of this stock is as low as 2%. Invest everything in the Andrew calculates the portfolio variance by adding the individual values of each stocks: Portfolio variance = 0. • Markowitz approach determines for the investor the efficient set of portfolio through three important variables, i. the two securities will be equally weighted. 5(0. 3. 5. A risky portfolio, X, has an expected return of 0. a) What is the standard deviation of a portfolio invested half in Dell and half in Microsoft? b) What is the standard deviation of a portfolio invested one-third in Dell, one-third in Microsoft and one-third in Treasury Bills? c) What is the standard deviation if the The standard deviation or portfolio variance is calculated by considering the actual covariance between securities in a portfolio. The relationship is expressed in the following way: Where: On a standard expected return versus standard deviation graph, investors will prefer portfolios that lie to the _____ the current investment opportunity set. Now, assume that the weights were revised so that the portfolio were 20% invested in a 79. standard deviation) that can be achieved at each level of expected return for a given set of risky securities. , equal to -1 C. 00% Artemis Inc. However, this is not correct--it is necessary to use a different formula, the one for σ that we used earlier, applied to the two-stock portfolio's returns. Thus, the investor is able to achieve a return of 9% and bring the risk to the minimum level. The formula for portfolio variance is given as: Var(R p) = w 2 1 Var(R 1) + w 2 2 Var(R 2) + 2w 1 w 2 Cov(R 1, R 2) Where Cov(R 1, R 2) represents the covariance of the two asset returns. 2 = 1/20(0. 4 = the standard deviation of Stock j. Sigma one squared, plus W two squared, Sigma two squared, and unfortunately, plus the term that I will use the red color for, that is two, W one W two. An investor plans to invest equal amounts in A and B. Managed to minimize any increase in risk relative to market benchmark. ωSmall,p ωADM,p σ[Rp(t)] E[Rp(t)]-0. The standard deviations of returns on these securities (in percentage terms) are: = 6, = 9, and = 10. III. 4 percent. 0 INVESTMENT PRODUCTS: NOT FDIC INSURED t NO BANK GUARANTEE t MAY LOSE VALUE Growth of $10,000 Class A shares Inception through Dec. The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. R 2 measures how closely the portfolio's performance matches the performance of its benchmark. Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. 8 8) The expected return on MSFT next year is 12% with a standard deviation of 20%. 1225 0. 7 % Charles Schwab In order to completely eliminate the risk (i. The variance can be written as follows - B. 6 Tracking error, a measure of risk, is defined as the standard deviation of the portfolio's excess return vs. 932 percent? Using Equation (1) we find that 23. The variance of a portfolio of three assets can be written as a function of the variances of each of the three assets, the portfolio weights on each and the correlations between pairs of the assets. The expected return on AAPL next year is 24% with a standard deviation of 30%. Calculate the expected returns and standard deviation of the two securities. is 1. Let’s take an example to understand the calculation. The standard deviation of A and B are 0. Change in Portfolio Proportion : If the amount of proportion of funds, invested in different stocks is changed e. The efficient frontier shows us the minimum risk (i. 6%). What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. 7%-1. This equation is normalized so that the result is a yield percentage that can be compared to investment returns, which allows the utility score Risk premium is the product of the market price of risk and the quantity of risk, and the risk is the standard deviation of the portfolio. 25. 6Q 4 calculate the beta of the standard deviation of its excess return: S(x,µ,Σ) = r(x,µ)−µrf σ(x,Σ). Then, he calculates the portfolio standard deviation: Portfolio standard deviation = Portfolio variance0. Suppose Miss Maple invested $2,500 in Security A and $3,500 in security B. 20 Portfolio 11. 16) + . 80% Bonds 8. C. vec)%*%sigma. 2% Health Care 13. 3% Deviation in Dec (A,B) = (2. 07268 In Figure 1. Since statements a and c are correct, the correct choice is statement e. What is the standard deviation of a security which has the following expected from FIN 465 at Cleveland State University Systematic and Unsystematic Risk Capital Asset Pricing Model Portfolio Theory (a) Reducing the Risk of a Portfolio vp = v1 + 2*x2*(c12-v1) + (x2^2)*(v1-2*c12+v2) The standard deviation of return (sp) will, as always, be the square root of the variance: sp = sqrt(vp) Throughout this section we will assume that asset 1 has less risk (v1&ltv2) and a smaller expected return (e1&lte2). 2 CMBS 14. More generally, the Portfolio risks can be calculated, like calculating the risk of single investments, by taking the standard deviation of the variance of actual returns of the portfolio over time. mat%*%m. greater than zero. e. e. 55%. 4 We must solve 10 + 40/N = 1. d. 7%. ii) expected return, systematic risk and unsystematic risk; and (iv) Sharpe ratio, Treynor ratio and Alpha of MFX, MFY and Portfolio Mix. Given, The standard deviation of stock A, ơ A = 15% Portfolio Variance Formula – Example #2. 21. The expected return and Beta of all investment in a portfolio is the weighted average of return and betas of all securities in the portfolio. The greater the standard deviation, the greater the fund’s volatility. -cannot be less than the weighted average of the standard deviations of the individual securities held in that portfolio. 00% 35% 13. 5% II. 8. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. c. You have a portfolio consisting solely of stock A and stock B. Suppose we are considering investing in three securities: X1, X2, and X3. The answer is b. A) less than +1. How much would a portfolio P(10), that levers the 500-stock portfolio, P(500), be expected to yield if P(500) were levered so that the standard deviation of the returns on portfolio P(10) is 23. 4) (0. 7 . Calculate the required rate of return for each stock. 8(25) = 20% Problem 10 a. The investor will make a return of higher than 7. Use the following data Standard deviation values are dependent on the price of the underlying security. B. 10 40% Security B 0. 8% C. 590 Chapter 11 Portfolio Concepts 2. These higher values are not a reflection of higher volatility, but rather a reflection of the actual price. Download PDF. 7%. 1. Download Full PDF Package. portfolio. 12 and a standard deviation of 0. 5% to 19. 0. 0% Communication Services 18. 1(. 0629 = 6. Turnover Ratio is the percentage of a portfolio's assets that have changed over the course of a year: (Lesser of purchases or sales)/ Assume the standard deviation of the return on the market portfolio to be 15%. B. What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. Looking at the input data, it might appear that the small excess expected return (13% rather than 10%) of Asset 2 does not justify the considerable extra risk (a standard deviation of 30% rather than 10%), and that an investor should therefore select a portfolio consisting only of Asset 1. 2. 0202 0 But when it comes to the standard deviation of this portfolio, the formula becomes a little bit worse. b. A: correlation = 1. 566 ing a portfolio from just two asset classes, government bonds and large-cap stocks. 0916%) 1/2 = 3. 23. 0 percent b. The larger the portfolio's standard deviation, the greater the portfolio's volatility. (i) The Sharpe ratio of the portfolio is 0. 3. Calculate the expected returns for portfolio AB, AC, and BC D. 4 % 17. Suppose that we consider forming equally weighted portfolios from securities, all of whose expected rates of return (E i) are 20 percent, whose standard deviations of rates of return are 20% and the correlation between the returns of any two securities (r i,j) is 0. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -. 2. Gruber (1991): Modern Portfolio Theory and Investment Analysis, 4th Edition, Wiley, NY, pp. 9. 20. ¥ Alternative derivation of global minimum variance portfolio The variance for stock ABC works out to 0. The expected return on AAPL next year is 24% with a standard deviation of 30%. If a fund's returns follow a normal distribution, then approximately 68 percent of the time they will fall within one standard Calculate the variance of the portfolio with equal proportions in both stocks using the portfolio returns and expected portfolio returns from answer c. 6% b) The NUAMBS Company Plc has q two security-portfolios, consisting of sixty percent (60%) investment in security A and forty percent (40%) investment in security B. For a portfolio (w,0) of risky assets only, we use the shorthand notation S(w,µ,Σ) = S(w,0,µ,Σ). 2 0. equal to 0 D. Risk What is the standard deviation of a portfolio of two stocks given the following data? Stock A has a standard deviation of 30%. 6%). Given less than perfect correlation, investing in the two III. (A criticism of the variance or standard deviation as a measure is discussed later in this entry. 6, p 23 = 0. Calculate the covariance between ABC company stock and the portfolio. Stock B has a standard deviation of 18%. 7) + (19/20)b b is average beta for other 19 stocks. Table 1 presents the six-year period of mean return and standard deviation, the skewness and the kurtosis of the individual assets. It is tempting to find the standard deviation of the portfolio as the weighted average of the standard deviations of the individual securities, as follows: σ p ≠ w i (σ i ) + w j (σ j ) = 0. 9 = 1. The standard deviation of a portfolio of two securities will be less than the weighted average of the standard deviation of the two securities when the correlation between the two securities +5 to 25 If the expected return of a portfolio is 15 percent and the standard deviation of the portfolio is 10 percent, then the 68 percent probability range is ____ percent. Diversification does not guarantee a profit or protect against a loss. Security B 20 0. 29% The standard deviation declines from 23. The endpoints (X and Y) for all the frontiers are the same, since at each endpoint the expected return and standard deviation are simply the expected return and standard deviation of either asset. Calculate the expected retum( r ^ p ), the standard deviation(σ p ), and the coefficient of variation (CV p ) for this portfolio and fill in the appropriate blanks in the table. 2) 2(0. 6. 05. 0000. 12 40% Security C 0. 4 to 23. A portfolio consisting of two risky securities that have a correlation of zero has a minimum variance portfolio that has a standard deviation equal to (a) The weighted average of the standard deviations of the two securities (b) -1 (c) 0 (d) Greater than 0 12. 2 Cash & Other Securities 0. The correlation between the two stocks is . References. 45%. = the standard deviation of the market. 16 4. The Stock Holdings In His Portfolio Are Shown In The Following Table: Stock Percentage Of Portfolio 20% Expected Return 6. Asset-Backed Securities 6. ) Two common stocks, consolidated Edison and Apple have the following expected return and standard deviation of return over the next year: Common stock Expected rate of return Standard deviation Consolidated Edison 12% 8% Apple 20% 15% Additionally, assume that the correlation coefficient of returns on the two securities is +0. 12. 6%, while B’s standard deviation is only 2. 1 and 0. 16)+0. 163, or 16. Are these funds as well diversified as possible? in portfolio risk as portfolio size increased. C. Suppose, if the market index moves by 5% on either side, the market price of securities in the portfolio will increase or decrease only by 2. If the investor sells the ABC company stock, he will invest the proceeds in risk-free government securities yielding 0:42% per month. The global minimum variance portfolio has a standard deviation that is always _____. Missing values are not allowed. Refer to question (a). 6. 75 to 0. 2)(0. 12) + . 0212) 1/2 σ A = . covariance term is positive, the portfolio standard deviation still is less than the weighted average of the individual security standard deviations, unless the two securities are perfectly positively correlated. The portfolio's σ depends jointly on (1) each security's σ and (2) the correlation between the securities' returns. g. 165 + 1/20(1. D)The standard deviation of a portfolio cannot be lower than the weighted average standard deviation of the securities held within the portfolio. , equal to 0 D. 02 Xuyang Ma July 27, 2013 Topic 3: Portfolio Theory with 2 Risky Assets 1. 25. 3. • There is a diversification effect - the σ of the portfolio is not the weighted average σ of the two assets (in this example, the weighted average s. The higher the standard variation of the daily gains in a stock, the more wildly it tends to In this video on Portfolio Standard Deviation, here we discuss its definition and learn how to calculate the standard deviation of the portfolio (three asset σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2w 1 w 2 ρ 1,2 σ 1 σ 2 Keep in mind that this is the calculation for portfolio variance. J. 7%. Suppose Miss Maple borrowed from her friend 40shares of security B, which is Portfolio Standard Deviation=10. The standard reference for conventions applicable to US securities. Calculate the covariance between ABC company stock and the portfolio. 0212 Which means the standard deviation is: σ A = (0. 9. Portfolio information in the charts is based on the fund's net assets. 2%. 06 = 0. If the standard deviation of the portfolio is 14. 17% and stock B has an average expected return of 6,24%, the portfolio standard deviation is 3,75% (check out the Portfolio Standard Deviation article on how to calculate the standard deviation of a portfolio). The proportions of these securities are w 1 = 0. A diversification benefit is a reduction in portfolio standard deviation of return through diversification without an accompanying decrease in expected return. 1253) 2 σ = 0. 60% for stocks ABC and XYZ respectively. 141% whereas the variance for stock XYZ works out to 0. Data shown in Table 2. (iii) If the portfolio were 50% invested in a risk-free asset and 50% invested in a risky asset X, its expected return would be 9. 17(0. A well diversified portfolio has σpM=βσ 43. 00% 45. 6 Agency Hybrids 0. You can invest in two different securities with the following characteristics: Security Expected Return Standard Deviation AA 14% 17% BB 24% 58% In the table provided in the answer sheet to Problem Set 2, enter the expected returns of your portfolio in the column labeled “Expected Return” and the standard deviation of your portfolio for each of the different correlations in the remaining (a) Calculate the expected return and standard deviation for the following portfolios: i. The standard deviation of a See full list on madfientist. 85 14% 3 15% 1. 0006 + 0. A. 2% Financials 20. You decide to sell a portion of stock A and use the proceeds to purchase shares of Stock D which has a standard deviation of 16 percent. Suppose you created a two-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. 3-ou the covariance of return between X1 and X3, σ2. 1 gives annual return distribution parameters for two hypothetical assets A and B. 00% 42. 23. 2. 1(10) = 11, or N = 40 Problem 9 The expected return on the new portfolio = 0. C)Diversification occurs when the correlation between two securities is +1. 2%. 1)(0. In case of three assets, the formula is: σ P = (w A2 σ A2 + w B2 σ B2 + w C2 σ C2 + 2w A w B σ A σ B ρ AB + 2w B w C σ B σ C ρ BC + 2w A w C σ A σ C ρ AC) 1/2. 0380, the correlation coefficient between the returns on Securities Analysis & Portfolio Management Presented By Kamrul Anam Khan Director, SEC Contents Part-A: Investment fundamentals Understanding investment Some definitions Sources and types of risk Risk-return trade-off in different types of securities Important considerations in investment process Part-B: Securities Analysis Securities analysis concept and types Framework of fundamental riskless, then the standard deviation of the portfolio (applying the variance rule to the portfolio return formula, rp(t) = wi,p ri(t) + (1-wi,p) rf (t), and taking the square root) is given by: >rp(t)] = |wi,p_ >ri(t)] where >ri(t)] is the standard deviation of the return on risky asset i in period t, Unformatted text preview: Solutions to Homework 2 , FINC-UB. 7%. For a portfolio that is 60% X and 40% risk-free asset: I. Since the baseline for Beta = 1 (usually the S&P Index), a number greater than one means the stock is riskier than the index, and a number less than one means that the stock is less risky. 42%. 14%. a. The exhibit shows the plotted means and standard deviations obtainable from portfolios of two perfectly positively correlated stocks. Statistical Estimation for Each Asset. The portfolio contains 60% of stock A and the correlation coefficient between the two stocks is -1. 70)(. If two and more assets have correlation of less than 1, the portfolio standard deviation is lower than the weighted The standard deviation of an investment is the square root of the variance – both measure portfolio risk. A short summary of this paper. D. You also may use covariance to find the standard deviation of a multi-stock portfolio. Rf = 10%, Rm = 15%, β = 0. R 2 is a proportion that Mayle, Jan (1994), Standard Securities Calculation Methods: Fixed Income Securities Formulas for Analytic Measures, 2 (1st ed. d. , a portfolio standard deviation of zero) in a two-asset portfolio, the correlation coefficient between the securities must be ____. Correlation The trade-off between risk and return for a portfolio depends not only on the expected asset returns and variances but also on the correlation of asset returns. 5 = 0. Systematic Risk Consider the following information: Standard Deviation Beta Security C 20% 1. 00% Cornell Industries Danforth Motors 15% 3. 8) The expected return on MSFT next year is 12% with a standard deviation of 20%. numeric(t(m. Volatility was calculated using the standard deviation, or historical measure of volatility, of the monthly returns for the respective The variance and standard deviation are conceptually equivalent; that is, the larger the variance or standard deviation, the greater the investment risk. 122 p p σ σ =+ + = == 8. 25 Security K 30% 0. An investor plans to invest equal amounts in A and B. Actively managed to maintain daily liquidity and to preserve capital. Security A's expected return is 10 percent while the expected return of B is 14 percent. 15) + . Determine the variance. 16. 0. 4(. (c) minimizes return for a given level of risk. . 9 % 10. Thus we can see that the Standard Deviation of Portfolio is 18% despite individual assets in the portfolio with a different Standard Deviation (Stock A: 24%, Stock B: 18%, and Stock C: 15%) due to the correlation between assets in the portfolio. 8% Consumer Staples 11. Market portfolio One of the first definitions of a well-diversified portfolio Variance = 0. 00 16% 2 30% 0. the benchmark expressed in percent. 79. The correlation between the two stocks is . Portfolio variance takes into account the weights and variances of each asset in a A. The volatility is best measured using standard deviation which can be calculated as follows: σ = (σ 2) 1/2 = (0. 0 B 0 0. This indicates it has low standard deviation. 0 0. Stock B has a standard deviation of 14%. ThePortfolio’s expected standard deviation, based on theseweights and thestatistics provided in theTablewas: ¾ P =[w2 1(¾ 1) 2+w 2 Introduction 1 1. 20. a. 3. Two assets a perfectly negatively correlated provide the maximum diversification benefit and hence minimize the risk. Solution Manual Investment Analysis & Portfolio Management by. 4% 12% 0. the security with the higher standard deviation will be weighted more heavily. Part 1. on margin) and short 50% of the risk-free asset. The larger the portfolio’s standard deviation, the greater the portfolio’s volatility. A portfolio is composed of two stocks, A and B. where, R P = expected return of portfolio R M = return on the market portfolio I RF = risk-free rate of interest σ M = standard deviation of the market portfolio 79. Now, we can compare the portfolio standard deviation of 10. undiversifiable risk – is the only reason that expected returns differ between securities 31 CAPM applies to portfolios as well as to individual securities for portfolios: – expected return: – beta: – variance and standard deviation (for a well-diversified portfolio): var s. Standard Deviation of a two Asset Portfolio. With a weighted portfolio standard deviation of 10. 6% Response Feedback: correct Question 16 0. 20(. A portfolio that combines a stock mutual fund and a bond mutual fund is an example. 2 percent. c If (1¡w) is negative, than our investment in the risk-free asset is a short position, which means that we have borrowed money. Explain. Correlation coe cient equals ˆ AB. 48%. 1215% and 3. 9. What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. 9. Which security should have the higher expected return? C because beta measures risk and its expected return Consider a risky portfolio consisting of two risky mutual funds: a bond fund of long-term debt securities, denoted D, and a stock fund, denoted E. 15. 5 Question: Andre Is An Amateur Investor Who Holds A Small Portfolio Consisting Of Only Four Stocks. You are given the following information concerning two stocks: --- A B Expected return 10% 14% Standard deviation of the for the standard deviation of a portfolio will get more complicated as the number of assets in the portfolio increases. Award: 10 out of 10. NOT FDIC INSURED • MAY LOSE VALUE • NO BANK GUARANTEE To calculate the standard deviation of a 2-asset portfolio, the formula is as follows: P ortf olio variance = (w2 A ∗σ2 A)+(w2 B ∗σ2 B)+(2∗wA ∗wB ∗σA ∗σB ∗ρAB) P o r t f o l i o v a r i a n c e = (w A 2 ∗ σ A 2) + (w B 2 ∗ σ B 2) + (2 ∗ w A ∗ w B ∗ σ A ∗ σ B ∗ ρ A B) Since its inception in November 2009, its standard deviation was over 2 percentage points less than the Bloomberg Barclays US Aggregate Bond Market index and nearly 12 percentage points less than tangent (optimal) portfolio has an expected return of 12. 65%)× (4. A portfolio consisting of about 30 randomly selected stocks. A higher standard deviation implies a wider predicted performance range and greater volatility. 25. Mutual Fund . 20(–0. Fahim Idris. Moreover, data tends to occur in a typical range under a normal distribution graph: Around 68% fall between -1 and 1; Around 95% fall between -2 and 2; Around 99% fall between -3 and 3; Standard Deviation in Thus, the true benefits of diversification are sensitive to the choice of risk measure. Suppose Miss Maple borrowed from her friend 40 shares of security B, which is currently sold at $50, Assume the following information the three securities: Correlation coefficients with std dev(%) А B C A 20 1. Portfolio standard deviation for a two-asset portfolio is given by the following formula: σ P = (w A2 σ A2 + w B2 σ B2 + 2w A w B σ A σ B ρ AB) 1/2. From Two Assets To Three Assets to n Assets. equal to -1 C. The CML equation is : R P = I RF + (R M – I RF)σ P /σ M. A portfolio is composed of two stocks, A and B. 0006 + 0. 1455) / . Standard deviation of the Stock A 25 percent. 18 β A = . is an arithmetic average of the standard In the above example, let’s say the standard deviation of the two assets are 10 and 16, and the correlation between the two assets is -1. 6 percent. Select the correct statement regarding the market portfolio. 3667. Express your answer in percent, but to Your portfolio is currently invested in three securities. 4) = 1. Standard deviation of a portfolio depends on the weight of each asset in the portfolio, standard deviation of individual investments and their mutual correlation coefficient. vec) > sig. 0 1. Alternatively, the percentage of portfolio fund that is invested in each security provides returns at a minimised Standard Deviation is an indicator of the portfolio's total return volatility, which is based on a minimum of 36 monthly returns. The beta for fund A is . For example, if the highest value in the IQ dataset had been 150 instead of 116, the SD would have gone up from 14. Investors can use standard deviation to predict a fund’s volatility. Calculate the standard deviations for portfolios AB, AC, and BC. 165 = (19/20)b. Next, we calculate the correlation coefficient for Stock ABC and XYZ returns. is a weighted average of the standard deviations of the individual securities held in the portfolio 2. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -. 10. 0 D) equal to -1. 3. The portfolio contains 40% of The holdings of the Rebalanced portfolio were rebalanced on a quarterly basis back to the Initial Index Weightings for each Primary Asset Class. 2 1. Calculate the: 1. Lower is better. If a test question asks for the standard deviation then you will need to take the square root of the variance calculation. When the expected returns, standard deviation, and correlations change slightly, the weights we obtain typically vary a lot. How-ever, since the 2 correlation coefficients are less than 1, we know the portfolio’s standard deviation will be less than 25 percent. 62% as the correlations declines from 0. But now we can only borrow at 7%. Alternatively, the formula can be written as: The expected return on a portfolio is the weighted average of the assets included in the portfolio and their expected returns. all in Z ii. Calculate the risk (standard deviation) of the following two-security portfolio if the correlation coefficient between the two securities is equal to 0. Stock A and Stock B are two real estate stock in a portfolio having a return of 6% and 11% and weight of stock A is 54% and the weight of Stock B is 46%. In a two-security minimum variance portfolio where the correlation between securities is greater than − 1. 3, w 2 = 0. its deviation from the portfolio required rate of return. 4 percent c. 3% U. 48, you can expect your return to be 10 points higher or lower than the average when you hold these two investments. Calculate the standard deviation of his new portfolio which includes the ABC company stock. 1455, or 14. Consider a portfolio of two stocks. 02 + 1/3 × 0. Babish & Co. 293 – . gmin = as. Example 1 Two risky asset portfolio information Table 1. 4 & 8. com The standard deviation of a security is synonymous with risk. The value of stock A is $60,000, and its standard deviation is 15%, while the value of stock B is $90,000, and its standard deviation is 10%. 0016 + 0. 578%. A nancial portfolio is an investment consisting of any collection of securities or assets eg stocks and bonds. Calculate the standard deviation of a portfolio weighted equally between the two securities if their correlation is: 1. and K Mutual Fund Ltd. 161)+0. The risk aversion coefficient is a number proportionate to the amount of risk aversion of the investor and is usually set to integer values less than 6, and 0. 12 (12%) For an IQ example (84, 84, 89, 91, 110, 114, and 116) where the mean is 98. 0. New Beta = 1. 0. 5(13. Securities with high prices, such as Google (±550), will have higher standard deviation values than securities with low prices, such as Intel (±22). This portfolio usually is not the optimal portfolio choice because the returns on this portfolio are very low relative to other alternative portfolio selections. 5) 0. Standard deviation was commonly used as a measure of risk in earlier studies (see for example Fisher and Lorie, 1970; Wagner Using either the correlation coefficient or the covariance, the Variance on a Two-Asset Portfolio can be calculated as follows: sd2 p = (wA)2s2 A + (wB)2s2 B + 2wAwBrA,B sAsB OR sd2 p = (wA)2s2 A + (wB)2s2 B + 2wAwB sA,B The Standard Deviation of the Portfolio equals the positive square root of the variance. Calculate the expected returns and standard deviations of the two securities. The standard deviation of return on a portfolio consisting of the small firm asset and ADM and its expected return can be indexed by the weight of the small firm asset in the portfolio. 14%. p(boom) = 2/3 and p(recession)=1/3 (Note that probabilities always add up to 1) E(RA) = 2/3 × 0. Portfolio beta Answer: b Diff: E 1. the benchmark expressed in percent. The expected returns and standard deviation of returns for two securities are as follows: Security Z Security Y Expected Return 15% 35% Standard Deviation 20% 40% The correlation between the returns is + . The standard deviation of a portfolio is: 1. 1% and the annualized standard deviation of the return was 24. E. 0240. To simplify the environment (and the math), we will only look at a portfolio with two risky assets. 9 2. gmin [1] 0. 16)2 +0:6(12:2¡11:16)2 +0:2(16:6¡11:16)2 = 21:22 Standard deviation= p 21:22= 4:61% c. It can hold investment types that are volatile on their own, but when combined, create a diversified portfolio with lower volatility than any of the individual parts. We compute the portfolio’s standard deviation based on the standard deviation and correlation assumptions  The standard deviation is computed in cell L34 and is given by the formula =J34*sigt. Variance Weight (in the portfolio) Security A 10 0. d. 24. Which of the following statements is true about this portfolio consisting of stock A and stock B. Investors 1, 2, 5, and 6 have the same correct estimates of expected returns for Securities A, B, E, and F, but they all have estimated the wrong expected returns for both Securities C and D As you can see, the standard deviation of the sample for Location A is only 2. 32(0. Nevertheless, we suspect most Number of securities in portfolio (N) Estimated portfolio variance 5 18 10 14 20 12 50 10. a. 2 % 22. 3%. Equity Market 15. 32 58. The standard deviation of her portfolio is 2. the standard deviation of a portfolio consisting two securities is sensitive to


The standard deviation of a portfolio consisting two securities is sensitive to