Unit 4 overflow all printed Flashcards
a) What are the coefficients of variation for Stocks A and B? (4 = 5 year -1)
b) What are the Sharpe ratios for Stocks A and B? Which stock has performed better on a risk-adjusted basis? Explain (4 = 5 year -1)
…………………………………………………………………………….?
Please note that the standard deviation calculation used here is for a sample (divided by n-1, where n is the number of observations).
a) For Stock A:
Mean = (20 + 30 - 2 + 6 + 18) /5 = 14.4%
[((20.0% - 14.4%) ^ 2(30.0% - 14.4%) ^ 2 + (-2.0% - 14.4%) ^ 2 + (6.0% - 14.4%) ^ 2 + (18.0% - 14.4%) ^ 2) /(5 - 1)]
converted to decimal form
sqrt([((.20-.144)^2 + (.30-.144)^2 + (-.02-.144)^2 + (.06-.144)^2 + (.18-.144)^2) / 4])
= 12.521981
Stock A’s coefficient of variation = 12.52%/14.4% = 0.87; CV a = 0.87
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b) For Stock B:
Mean =
(25 ÷ 18 ÷ 50 + 10 + 21.5) / 5 = 24.9%
Standard Deviation =
sqrt[((25 -24.9)^2 + (18-24.9)^2 +
(50- 24.9)^2 + (10- 24.9)^2 + (21.5-24.9)^2) / 4]
= 15.09%
Stock B’s coefficient of variation = 15.09%/ 24.9% = 0.61; CV = 0.61
An investment has a 50% chance of producing a 20% return, a 25% chance of producing an 8% return, and a 25% chance of producing a −12% return. What is its expected return …………………………………………………………………………….?
The expected return is calculated by multiplying each possible return by the probability of that return, then adding up these expected returns.
So, the expected return would be:
(0.50 * 20%) + (0.25 * 8%) + (0.25 * -12%) = 10% + 2% - 3% = 9%
An investor has a two-stock portfolio with $25,000 invested in Stock X and $50,000 invested in Stock Y. X’s beta is 1.50, and Y’s beta is 0.60. What is the beta of the investor’s portfolio …………………………………………………………………………….?
So, the beta of the portfolio would be:
($25,000 / $75,000) *1.50 + ($50,000 / $75,000) *0.60 =
0.33 * 1.50 ÷ 0.67 * 0.60 = 0.50 + 0.40 = 0.90
The risk-free rate is 3%, and the market risk premium (rM - rRF) is 4%. Stock A has a beta of 1.2, and Stock B has a beta of 0.8
a). What is the required rate of return on each stock?
rA = rRF + RPM (ba)
= 3% + 4% (1.2)
= 7.8%
rB = IRF + RPm (bB)
= 3% + 4% (0.8)
= 6.2%
b) Assume that investors become less willing to take on risk (i.e., they become more riskaverse), so the market risk premium rises from 4% to 6%. Assume that the risk-free rate remains constant. What effect will this have on the required rates of return on the two stocks …………………………………………………………………………….?
a) Capital Asset Pricing Model
(CAPM), which is:
Required return =
Risk-free rate + Beta * Market risk premium
For Stock A: Required return = 3% + 1.2 * 4% = 7.8%
For Stock B:
Required return = 3% + 0.8 * 4% = 6.2%
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b) If the market risk premium rises from 4% to 6%, the required rates of return on the stocks will increase as well.
For Stock A:
New required return = 3% + 1.2 * 6% = 10.2%
For Stock B:
New required return = 3% + 4.8 * 6%= 7.8%
A stock has a beta of 1.2. Assume that the risk-free rate is 4.5%, and the market risk premium is 5%. What is the stock’s required rate of return …………………………………………………………………………….?
Capital Asset Pricing Model
(CAPM), which is:
Required return = Risk-free rate +
Beta * Market risk premium
For this stock:
Required return = 4.5% + 1.2 * 5% = 10.5%
REALIZED RATES OF RETURN Stocks A and B have the following historical returns:
PART 1 of 2
a). Calculate the average rate of return for each stock during the period 2016 through 2020. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been in each year from 2016 through 2020? What would the average return on the portfolio have been during that period
d) Looking at the annual returns on the two stocks, would you guess that the correlation coefficient between the two stocks is closer to +0.8 or to -0.8?
…………………………………………………………………………….?
For Stock A:
(-24.25 + 18.50 + 38.67 + 14.33 + 39.13) / 5 = 17.28%
For Stock B:
(5.50 + 26.73 + 48.25 - 4.50 + 43.86) / 5 = 23.97%
b. If someone held a portfolio consisting of 50% of Stock A and 50% of Stock B, the realized rate of return on the portfolio in each year from 2016 through 2020 would be the average of the returns of the two stocks in that year.
For 2016: (-24.25 + 5.50) / 2 = -9.38%
For 2017: (18.50 + 26.73) / 2= 22.62%
For 2018: (38.67 + 48.25) / 2 = 43.46%
For 2019: (14.33 - 4.50) / 2 = 4.92%
For 2020: (39.13 + 43.86) / 2 = 41.50%
The average return on the portfolio during the period 2016 through 2020 would then be the average of these yearly returns:
(-9.38 + 22.62 + 43.46 + 4.92 + 41.50) / 5 = 20.62%
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d) Because the risk reduction from diversification is small (betaAB falls only to 22.96%), the most likely value of the correlation coefficient is 0.8. If the correlation coefficient were -0.8, the risk reduction would be much larger. In fact, the correlation coefficient between Stocks A and B is 0.76.
b) Calculate the standard deviation of returns for each stock and for the portfolio PART 2 of 2
c) Assume the risk-free rate during this time was 3.5%. What are the Sharpe ratios for Stocks A and B and the portfolio over this time period using their average returns?
…………………………………………………………………………….?
First, we need to calculate the mean returns for each stock and the portfolio (Previous problem):
For Stock A: 17.28%
For Stock B: 23.97%
For the Portfolio: 20.62%
Next, we calculate the variance for each:
For Stock A:
[(-24.25 - 17.28)^2 + (18.50 - 17.28)^2 + (38.67 - 17.28)^2 + (14.33 - 17.28)^2 + (39.13 - 17.28)^2] /
5 -1(4) = 667.4716/667.47
For Stock B:
[(5.50 - 23.97) ^2 + (26.73 - 23.97)^2 + (48.25 - 23.97)^2 + (-4.50 - 23.97)^2 + (43.86 - 23.97)^2] / 5-1 (4) =
536.107475/536.11
For the Portfolio:
[(-9.38 - 20.62)^2 + (22.62 - 20.62)^2 + (43.46 - 20.62)^2 + (4.92 -20.62)^2 + (41.50 - 20.62)^2] / 5-1 (4) =
527.0325/527.03
Finally, we take the square root of each variance to get the standard deviation:
For Stock A: sqrt(667.47)
= 25.835472/ 25.84%
For Stock B: sqrt(428.89)
= 23.154049 / 23.15%
For the Portfolio: sqrt(527.03)
= 22.957134 / 22.96%
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c) The Sharpe ratio is calculated as (Return - Risk-free rate) / Standard deviation
For Stock A:
Sharpe Ratio = (17.28% - 3.5%) / 25.84% = 0.533282/0.5333
For Stock B:
Sharpe Ratio = (23.97% - 3.5%) / 23.15% =
0.884233/0.8842
For the Portfolio:
Sharpe Ratio = (20.62% - 3.5%) /22.96% = 0.745645/0.7456
BETA AND THE REQUIRED RATE OF RETURN ECRI Corporation is a holding company with four main subsidiaries. The percentage of its capital invested in each of the subsidiaries (and their respective betas) is as follows:
a) What is the holding company’s beta
b) If the risk-free rate is 4% and the market risk premium is 5%, what is the holding company’s required rate of return?
…………………………………………………………………………….?
a) So, to calculate the holding company’s beta, we multiply the beta of each subsidiary by the percentage of the company’s capital that is invested in that subsidiary, and then sum these products:
Holding Company’s Beta =
(0.60 * 0.70) + (0.25 * 0.90) + (0.10 * 1.30) + (0.05 * 1.50) = 0.85
________________________________________________________
B) So, the holding company’s required rate of return is:
Required Rate of Return = Risk- Free Rate + (Beta * Market Risk Premium)
= 4% + (0.85 * 5%)
= 4% + 4.25%
= 8.25%.
c) ECRI is considering a change in its strategic focus; it will reduce its reliance on the electric utility subsidiary, so the percentage of its capital in this subsidiary will be reduced to 50%. At the same time, it will increase the firm’s reliance on the international/special projects division, so the percentage of its capital in that subsidiary will rise to 15%. What will the company’s required rate of return be after these changes …………………………………………………………………………….?
c)
First, we need to recalculate the company’s beta given the new capital allocations:
New Beta =
(0.50 * 0.70) + (0.25 * 0.90) + (0.10 * 1.30) + (0.15 * 1.50) = 0.93
New Required Rate of Return =
Risk-Free Rate + (New Beta * Market Risk Premium)
= 4% + (0.93 * 5%)
= 4% + 4.65%
= 8.65%
EXPECTED RETURN A stock’s returns have the following distribution:
part 1 of 2
Assume the risk-free rate is 2%. Calculate the stock’s expected return, standard deviation, coefficient of variation, and Sharpe ratio
…………………………………………………………………………….?
A)
Expected Return = (0.1-30) + (0.1-14) + (0.311) + (0.320) + (0.245) = 13.9
_______________________________________________________
standard deviation = Variance =
[0.1(-30 - 13.9)^2 + 0.1(-14-13.9)^2 +
0.3(11-13.9)^2 +
0.3* (20-13.9)^2 +
0.2* (45-13.9)^2] = 477.69
& then sqaureroot 477.69 = 21.86
_______________________________________________________
Coefficient of Variation = Standard
Deviation / Expected Return =
21.86% / 13.9% = 1.572662 / 1.57%
_______________________________________________________
Sharpe Ratio = (Expected Return -
Risk-Free Rate) / Standard
Deviation = (13.9% - 2%) /21.86% = 0.544373 / 0.54
B) An individual has $20,000 invested in a stock with a beta of 0.6 and another $75,000 invested in a stock with a beta of 2.5. If these are the only two investments in her portfolio, what is her portfolio’s beta …………………………………………………………………………….?
So, to calculate the portfolio’s beta, we multiply the beta of each investment by the proportion of the portfolio’s total value that is invested in that investment, and then sum these products:
Total investment = $20,000 + $75,000 = $95,000
Proportion of portfolio in first
stock = $20,000 / $95,000 = 0.2105 (approximately)
Proportion of portfolio in second
stock = $75,000 / $95,000 = 0.7895 (approximately)
Portfolio’s Beta = (0.2105 * 0.6) +
(0.7895 * 2.5) = 2.10 (approximately)
Assume that the risk-free rate is 5.5% and the required return on the market is 12%. What is the required rate of return on a stock with a beta of 2
part 2 of 2
…………………………………………………………………………….?
c)
So, the required rate of return on the stock is:
Required Rate of Return =
Risk- Free Rate + (Beta * Market Risk Premium)
= 5.5% + (2 * (12% - 5.5%))
= 5.5% + (2 * 6.5%)
= 5.5% + 13%
c)= 18.5%
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d) EXPECTED AND REQUIRED RATES OF RETURN Assume that the risk-free rate is 3.5% and the market risk premium is 4%. What is the required return for the overall stock market? What is the required rate of return on a stock with a beta of 0.8?
d) Required Return for the Market =
Risk-Free Rate + Market Risk
Premium = 3.5% + 4%
= 7.5%
Required Return on the Stock =
Risk-Free Rate + (Beta * Market
Risk Premium)
= 3.5% + (0.8 * 4%)
= 3.5% + 3.2%
= 6.7%
BETA AND REQUIRED RATE OF RETURN A stock has a required return of 9%, the risk-free rate is 4.5%, and the market risk premium is 3%.
a) What is the stock’s beta?
b) If the market risk premium increased to 5%, what would happen to the stock’s required rate of return? Assume that the risk-free rate and the beta remain unchanged.
…………………………………………………………………………….?
a) The beta of a stock can be calculated by rearranging the Capital Asset Pricing Model
(CAPM) formula. The CAPM formula is:
Required Return = Risk-Free Rate + (Beta * Market Risk Premium)
Rearranging for Beta gives:
Beta = (Required Return - Risk- Free Rate) / Market Risk Premium
Substituting the given values into this formula gives:
Beta = (9% - 4.5%) / 3%= 1.5
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b) We can calculate the new required rate of return using the Capital Asset Pricing Model (CAPM) formula:
Required Return = Risk-Free Rate + (Beta * Market Risk Premium)
Substituting the given values into this formula gives:
Required Return = 4.5% + (1.5 * 5%) = 12%
EXPECTED RETURNS Stocks A and B have the following probability distributions of expected future returns:
a) Calculate the expected rate of return, §B, for Stock B (§A = 12%).
b) Calculate the standard deviation of expected returns, betaa, for Stock A (oB(beta) = 20.35%). Now calculate the coefficient of variation for Stock B. Is it possible that most investors will regard Stock B as being less risky than Stock A? Explain.
c)Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Are these calculations consistent with the information obtained from the coefficient of variation calculations in part b? Explain.
…………………………………………………………………………….?
a) Expected Return for stock B= (0.1*-35%) +
(0.2 * 0 %) + (0.4 * 20%) + (0.2 * 25%) + (0.1 * 45%) = 0.14/14%
_____________________________________________________________
b) Coefficient of Variation for Stock B
= Standard Deviation / Expected Return =
20.35% / 14% = 1.453571/1.45%
standard deviation= First, let’s calculate the expected return for Stock A, which is given as 12%.
Next, we calculate the variance:
Variance = [0.1(-10-12)^2 + 0.2 (2-12)^2 + 0.4(12-12)^2 +
0.2 (20-12)^2 + 0.1* (38-12)^2] = 148.8
now squareroot 148.8 = 12.198361/12.20
_____________________________________________________________
c) For Stock A:
Sharpe Ratio = (Expected Return -
Risk-Free Rate) / Standard Deviation =
(12% - 2.5%) / 12.2% = 0.778689/0.78 (approximately)
For Stock B:
Sharpe Ratio = (Expected Return -
Risk-Free Rate) / Standard Deviation =
(14% - 2.5%) / 20.35% = 0.565111 (approximately)
PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.82 million investment fund. The fund consists of four stocks with the following investments and betas:
If the market’s required rate of return is 8% and the risk-free rate is 4%, what is the fund’s required rate of return?
…………………………………………………………………………….?
Stock Investment Beta
A $ 460,000 1.50
B $ 500,000 (0.50)
C $1,260,000 1.25
D $2,600,000 0.75
First, we need to calculate the portfolio’s beta, which is the weighted average of the betas of the individual stocks in the portfolio. The weights are the proportions of the portfolio’s total value that are invested in each stock.
Portfolio Beta =
(460,000/4,820,000)1.50 +
(500,000/4,820,000)(-0.50) +
(1,260,000/4,820,000)1.25 +
(2,600,000/4,820,000)0.75 = 0.822614
Then, we can use the CAPM to calculate the required rate of return:
Required Rate of Return = Risk- Free Rate + (Portfolio Beta * Market Risk Premium)
=4% + (0.822614 * (8% - 4%)) —> .04 + (0.822614 * (.08 - .04))
= 0.072905/7.3%
a) BETA COEFFICIENT Given the following information, determine the beta coefficient for Stock L that is consistent with equilibrium: §1 = 10.5%; rRF = 3.5%; rM = 9.5%
b) REQUIRED RATE OF RETURN Stock R has a beta of 2.0, Stock S has a beta of 0.45, the required return on an average stock is 10%, and the risk-free rate of return is 5%. By how much does the required return on the riskier stock exceed the required return on the less risky stock?
…………………………………………………………………………….?
a) The beta coefficient for a stock can be calculated using the Capital Asset Pricing Model (CAPM), which states that the expected return on an investment is equal to the risk-free rate plus the product of the investment’s beta and the market risk premium (the difference between the expected return on the market and the risk-free rate).
Rearranging the CAPM formula to solve for beta gives:
Beta = (Expected Return - Risk-
Free Rate) / Market Risk Premium
Substituting the given values into this formula gives:
Beta = (10.5% - 3.5%) / (9.5% - 3.5%) = 1.166667/1.17
b) For Stock R (the riskier stock):
Required Return = Risk-Free Rate
+ (Beta * Market Risk Premium)
= 5% + (2.0 * (10% - 5%))
= 5% + 10%
= 15%
For Stock S (the less risky stock):
Required Return = Risk-Free Rate
+ (Beta * Market Risk Premium)
= 5% + (0.45 * (10% - 5%))
= 5% + 2.25%
= 7.25%
The difference between the required return on the riskier stock and the less risky stock is:
15% - 7.25% = 7.75%
So, the required return on the riskier stock exceeds the required return on the less risky stock by 7.75%.
a) CAPM AND REQUIRED RETURN Beale Manufacturing Company has a beta of 1.1, and Foley Industries has a beta of 0.30. The required return on an index fund that holds the entire stock market is 11%. The risk-free rate of interest is 4.5%. By how much does Beale’s required return exceed Foley’s required return
…………………………………………………………………………….?
a)
For Beale Manufacturing Company:
Required Return = Risk-Free Rate
+ (Beta * Market Risk Premium)
= 4.5% + (1.1 * (11% - 4.5%))
= 11.65%
For Foley Industries:
Required Return = Risk-Free Rate
+ (Beta * Market Risk Premium)
= 4.5% + (0.30 * (11% - 4.5%))
= 6.45%
The difference between Beale’s required return and Foley’s required return is:
11.65% - 6.45% = 5.2% (final anwser)
CAPM, PORTFOLIO RISK, AND RETURN Consider the following information for Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)
Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate (rRF) is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)
PART 1 of 3
a) What is the market risk premium (rm - rRF) …………………………………………………………………………….?
The market risk premium (rm - rRF) can be calculated using the Capital Asset Pricing Model
(CAPM) formula:
ri = rRF + bi * (rm - rRF)
We can rearrange the formula to solve for the market risk premium (rm - rRF):
rm - rRF = (ri - rRF) / bi
We can use the information for any of the stocks to calculate the market risk premium. For example, using the information for Stock A:
rm - rRF = (9.55% - 5.5%) / 0.9
rm - rRF = 4.5%
So, the market risk premium is 4.5%
CAPM, PORTFOLIO RISK, AND RETURN Consider the following information for Stocks A, B, and C. The returns on the three (1/3) stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)
Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate (rRF) is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)
PART 2 of 3
b) What is the beta of Fund P?
…………………………………………………………………………….?
1/3rd explanation =
The 1/3 represents the proportion of the fund’s investment in each of the three stocks. According to the information provided, Fund P has one-third of its funds invested in each of the three stocks. This means that the weight (w) of each stock in the portfolio is 1/3 or approximately 0.3333 when expressed as a decimal
The beta of a portfolio (or a fund in this case) is the weighted average of the betas of the individual assets in the portfolio.
Given that Fund P has one-third of its funds invested in each of the three stocks, the beta of Fund P (bP) can be calculated as follows:
bP = wAbA + wBbB + wC*bC
where:
WA, wB, and wC are the weights of Stocks A, B, and C in the portfolio (which are all 1/3 in this case), and
bA, bB, and bC are the betas of Stocks A, B, and C.
Substituting the given values into the formula:
bP = (1/3)0.9 + (1/3)1.1 + (1/3)*1.6
bP= 1.2
CAPM, PORTFOLIO RISK, AND RETURN Consider the following information for Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)
PART 3 of 3
Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate (rRF) is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)
c) What is the required return of Fund P?
…………………………………………………………………………….?
The required return of a portfolio (or a fund in this case) can be calculated using the Capital Asset
Pricing Model (CAPM) formula:
ri = rRF + bi * (rm - rRF)
We’ve already calculated the beta of Fund P (P) as 1.2. The risk-free rate (rRF) is given as 5.5%. The market risk premium (rm - rRF)
was calculated as 4.5% in a previous step.
Substituting these values into the formula:
ri = rRF + bP * (rm - rRF)
ri = 5.5% + 1.2 * 4.5%
ri = 10.9
PORTFOLIO BETA A mutual fund manager has a $20 million portfolio with a beta of 1.7. The risk-free rate is 4.5%, and the market risk premium is 7%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund’s required return to be 15%. What should be the average beta of the new stocks added to the portfolio
…………………………………………………………………………….?
The required return of the portfolio is calculated using the Capital Asset Pricing Model (CAPM) formula:
Required Return = Risk-free rate + Beta * Market Risk Premium
Given that the manager wants the fund’s required return to be 15%, the risk-free rate is 4.5% and the market risk premium is 7%, we can rearrange the formula to solve for the new beta:
Beta = (Required Return - Risk- free rate) / Market Risk Premium
Before the additional investment, the portfolio’s value is $20 million and its beta is 1.7. After the additional investment, the portfolio’s value will be $25 million (20mil + 5mil). The new average beta of the portfolio will be a weighted average of the old and new betas, with weights based on the portfolio values.
Let’s denote the new beta as B.
The weighted average beta will be:
(Required Return - Risk-free rate) / Market Risk Premium
(20/25) * 1.7 + (5/25) * B =
Substituting the given values:
(20/25) * 1.7 + (5/25) *B = (15% - 4.5%) / 7%
Solving for B:
B = [(15% - 4.5%) / 7% - (20/25)*1.7] * (25/5)
B= 0.7 (Attached REF)
Calculate the average rate of return for each stock during the period 2016 through 2020
…………………………………………………………………………….?
part 1 of 4
The average rate of return for a stock over a period of time is calculated by adding up all the annual returns and then dividing by the number of years.
For Stock A:
Average Return A =
[(- 18.00 + 33 + 15 - 0.5 + 27) / 5] = 11.3%
For Stock B:
Average Return B =
[(- 14.5 + 21.8 + 30.5 - 7.6 + 26.3) / 5] = 11.3%
Therefore, the average rate of return for Stock A from 2016 through 2020 is approximately 11.30%, and for Stock B is
11.30%
Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? What would the average return on the portfolio have been during this period …………………………………………………………………………….?
part 2 of 4
The realized rate of return on the portfolio for each year would be the average of the returns of Stock A and Stock B, since the portfolio is equally weighted.
For 2016: (-18.00% - 14.5%) / 2 = -16.25%
For 2017: (33% + 21.8%) / 2 = 27.4%
For 2018: (15% + 30.5%) / 2 = 22.75%
For 2019: (-0.5% - 7.6%) / 2 = -4.05%
For 2020: (27% + 26.3%) / 2 = 26.65%
The average return on the portfolio during this period would be the average of these annual returns:
Average Portfolio Return =
[(-16.25% + 27.4% + 22.75% - 4.05% + 26.65%) / 5] =
rp avg = .113 / 11.3%
Calculate the standard deviation of returns for each stock and for the portfolio
—> portfolio consisting of 50% of Stock A and 50% of Stock B. part 3 of 4
…………………………………………………………………………….?
Return for 2017 = sum(weight * return)
= 50% × (-18.00) + 50% × (- 14.50)
= −16.25
Return for 2018 = sum (weight * return)
= 50% × 33.00 + 50% × 21.80
=27.4
Return for 2019 = sum (weight * return)
= 50% × 15.00 + 50% × 30.50
= 22.75
Return for 2020 = sum(weight * return)
= 50% × (-0.50) + 50% × (-7.60)
= −4.05
Return for 2021 = sum(weight * return)
= 50% × 27.00 + 50% × 26.30
= 26.65
The average return on the portfolio = Total of average returns/Number of years:
−16.25 + 27.4 + 22.75 + (−4.05) + 26.65 / 5= 11.3
–> USING average rate of return for each stock calculated from part 1 = 11.3
Stock A/RED = sqrt((sum(return - average return)^2)/(n - 1))
step1)= (-18.00 - 11.3)^2 + (33.00 - 11.3)^2 + (15.00 -11.3)^2 + (-0.50 - 11.3)^2 + (27.00-11.3)^2 / 5 -1 (n -1)=4
= 1728.8
step2) 1728.8 / 4 = 432.2
step3) sqrt(432.2) = 20.789420 / Sa= 20.8
_______________________________________________________
Stock B/BLUE = sqrt((sum(return - average return)^2)/(n - 1))
step1) = (-14.50 - 11.3)^2 + (21.80 - 11.3)^2 + (30.50 -11.3)^2 + (-7.60 - 11.3)^2 + (26.50 -11.3)^2 / 5 -1 (n -1)=4
=1732.78
step2)= 1732.78 / (5-1) = 433.195
step3)= sqrt(433.195)= 20.813337 / Sb= 20.8
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Portfolio = sqrt((sum(return - average return)2) / (n - 1))
step1) =
(−16.25 - 11.3)^2 + (27.4 - 11.3)^2 + (22.75 -11.3)^2 + (-4.05 - 11.3)^2 + (26.65 -11.3)^2 / 5 -1 (n -1)=4
= 1620.56
step 2) 1620.56 / 4 = 405.14
step3) sqrt(405.14) = 20.128090 / 20.1
SECURITY MARKET LINE You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks: PART 1 OF 2
…………………………………………………………………………….?
First, we need to calculate the portfolio’s beta, which is a weighted average of the individual stock betas. The weights are the proportion of the portfolio’s value invested in each stock.
Portfolio Beta =
(Weight of Stock A * Beta of Stock A) + (Weight of Stock B * Beta of Stock B) + (Weight of Stock C * Beta of Stock C) + (Weight of Stock D * Beta of Stock D) + (Weight of Stock E * Beta of Stock E
The total value of the portfolio is $160 million + $120 million + $80 million + $80 million + $60 million
= $500 million.
RED
So, the weights are:
Stock A = $160 million / $500 million = 0.32,
Stock B = $120 million / $500 million = 0.24,
Stock C = $80 million / $500 million = 0.16,
Stock D = $80 million / $500 million = 0.16,
Stock E = $60 million / $500 million = 0.12.
ORANGE Portfolio Beta =
(0.32 * 0.5) + (0.24 * 1.2) + (0.16 * 1.8) + (0.16 * 1.0) + (0.12 * 1.6) = 1.088
Next, we use the Capital Asset Pricing Model (CAPM) to calculate the required rate of return:
Required Return = Risk-free rate + Portfolio Beta * Market Risk Premium
Next, we use the Capital Asset Pricing Model (CAPM) to calculate the required rate of return:
Required Return = Risk-free rate + Portfolio Beta * Market Risk Premium
The market risk premium is the expected market return minus the risk-free rate. The expected market return is a weighted average of the possible market returns, with the weights being the probabilities:
YELLOW Expected Market Return = (0.1 * -28%) + (0.2 * 0%) + (0.4 * 12%) + (0.2 * 30%) + (0.1 * 50%) = 13%
So, the market risk premium is
13% - 6% = 7%.
Finally, we substitute these values into the CAPM formula:
Required Return = 6% + 1.088 * 7% = 0.13616%
Therefore, Kish’s required rate of return is 13.616%
Bartman Industries’s and Reynolds Inc.’s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 2015–2020. The Winslow 5000 data are adjusted to include dividends.
Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index. Then calculate each entity’s average return over the 5-year period …………………………………………………………………………….?
PART 1 of 2 (rates of returns)
The annual rate of return can be calculated using the following formula:
Annual Rate of Return = (Ending Price - Beginning Price + Dividends) / Beginning Price
Let’s calculate the annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index:
1. Bartman Industries:
2020: (17.25 - 14.75 + 1.15) / 14.75 = 0.247458 or 24.75%
2019: (14.75 - 16.50 + 1.06) / 16.50 = -0.041818 or -4.18%
2018: (16.50 - 10.75 + 1.00) / 10.75 = 0.627907 or 62.79%
2017: (10.75 - 11.37 + 0.95) / 11.37 = 0.029024 or 2.90%
2016: (11.37 - 7.62 + 0.90) / 7.62 = 0.610236 or 61.02%
- Reynolds Inc.:
2020: (48.75 - 52.30 + 3.00) / 52.30 = -0.010516 or
- 1.05%
2019: (52.30 - 48.75 + 2.90) / 48.75 = 0.132308 or 13.23%
2018: (48.75 - 57.25 + 2.75) / 57.25 = -0.100437 or -10.04%
2017: (57.25 - 60.00 + 2.50) / 60.00 = -0.004167 or -0.42%
2016: (60.00 - 55.75 + 2.25) / 55.75 = 0.116592 or 11.66%
- Winslow 5000 Index:
2020: (11,663.98 - 8,785.70) / 8,785.70 = 0.327610 or 32.76%
2019: (8,785.70 - 8,679.98) / 8,679.98 = 0.012180 or 1.22%
2018: (8,679.98 - 6,434.03) / 6,434.03 = 0.349074 or 34.91%
2017: (6,434.03 - 5,602.28) / 5,602.28 = 0.148466 or 14.85%
2016: (5,602.28 - 4,705.97) / 4,705.97 = 0.1905 or 19.05%
Bartman Industries’s and Reynolds Inc.’s stock prices and dividends, along with the Winslow 5000 Index, are shown here for the period 2015–2020. The Winslow 5000 data are adjusted to include dividends.
Use the data to calculate annual rates of return for Bartman, Reynolds, and the Winslow 5000 Index. Then calculate each entity’s average return over the 5-year period
…………………………………………………………………………….?
PART 2 of 2 (average return over the 5-year period)
PART 2 of 2 (average return over the 5-year period)
The average return over the 5-year period can be calculated by adding up the annual returns and dividing by the number of years:
1. Bartman Industries: (24.75% - 4.18% + 62.79% + 2.90% + 61.02%) /5 = 0.29456 / 29.46%
- Reynolds Inc: (-1.05% + 13.23% - 10.04% - 0.42% + 11.66%) / 5 = 2.68%
- Winslow 5000 Index: (32.76% + 1.22% + 34.91% + 14.85% + 19.05%) / 5 = 20.56%
b) Calculate the standard deviations of the returns for Bartman, Reynolds, and the Winslow 5000
c) Calculate the coefficients of variation for Bartman, Reynolds, and the Winslow 5000.
d) Assume the risk-free rate during this time was 3%. Calculate the Sharpe ratios for Bartman, Reynolds, and the Index over this period using their average returns.
Spreadsheet ANS-REF Formulas
standard deviation ALT Formula = STDEV.P
