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Some investors use the Sharpe ratio as a way of comparing the benefits of owning shares of stock in a company to the risks. The Sharpe ratio of a stock is defined as the ratio of the difference between the mean return on the stock and the mean return on government bonds (called the risk-free rate rf ) to the SD of the returns on the stock.
The mean return on government bonds is rf = 0.03% per day.
The table below describes the daily return of three stocks.
Date |
APPLE |
TESLA |
GM |
01/10/2020 |
0.85% |
4.46% |
2.67% |
02/10/2020 |
-3.23% |
-7.38% |
0.26% |
05/10/2020 |
3.08% |
2.55% |
1.64% |
06/10/2020 |
-2.87% |
-2.75% |
-1.81% |
07/10/2020 |
1.70% |
2.73% |
4.01% |
08/10/2020 |
-0.10% |
0.15% |
1.87% |
09/10/2020 |
1.74% |
1.90% |
-0.16% |
12/10/2020 |
6.35% |
1.91% |
0.16% |
13/10/2020 |
-2.65% |
0.98% |
-1.06% |
14/10/2020 |
0.07% |
3.28% |
-0.63% |
15/10/2020 |
-0.40% |
-2.69% |
2.90% |
16/10/2020 |
-1.40% |
-2.05% |
2.64% |
19/10/2020 |
-2.55% |
-2.01% |
-0.30% |
20/10/2020 |
1.32% |
-2.06% |
6.75% |
21/10/2020 |
-0.54% |
0.17% |
0.48% |
22/10/2020 |
-0.96% |
0.75% |
4.58% |
23/10/2020 |
-0.61% |
-1.21% |
-1.55% |
26/10/2020 |
0.01% |
-0.08% |
-2.74% |
27/10/2020 |
1.35% |
1.05% |
-2.60% |
28/10/2020 |
-4.63% |
-4.39% |
-2.29% |
29/10/2020 |
3.71% |
1.18% |
2.35% |
30/10/2020 |
-5.60% |
-5.55% |
-1.03% |
02/11/2020 |
-0.08% |
3.21% |
0.06% |
03/11/2020 |
1.54% |
5.84% |
2.32% |
04/11/2020 |
4.08% |
-0.69% |
-0.31% |
05/11/2020 |
3.55% |
4.06% |
5.39% |
06/11/2020 |
-0.29% |
-1.86% |
0.89% |
09/11/2020 |
-2.00% |
-2.02% |
3.98% |
10/11/2020 |
-0.30% |
-2.59% |
5.44% |
11/11/2020 |
3.04% |
1.65% |
-1.27% |
12/11/2020 |
-0.23% |
-1.29% |
-3.06% |
(a) Find the Sharpe ratio of stock in these three companies. Which looks best from this investment point of view?
(b) How does the Sharpe ratio differ from the type of standardizing used to form z-scores?
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Step by stepSolved in 3 steps with 4 images
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- The following table shows betas for several companies. Calculate each stock's expected rate of return using the CAPM. Assume the risk-free rate of interest is 4%. Use a 7% risk premium for the market portfolio. Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Company. Caterpillar Apple Johnson & Johnson Consolidated Edison Beta 0.98 1.35 0.69 0.13 Cost of Capital % % %arrow_forwardSuppose Johnson & Johnson and the Walgreen Company have the expected returns and volatilities shown below, with a correlation of 22.4%. Johnson & Johnson Walgreen Company E [R] 6.5% 10.7% SD [R] 15.5% 19.9% For a portfolio that is equally invested in Johnson & Johnson's and Walgreen's stock, calculate: a. The expected return. b. The volatility (standard deviation). a. The expected return. The expected return of the portfolio is %. (Round to one decimal place.)arrow_forwardThe Swanson Corporation's common stock has a beta of 1.6. If the risk-free rate is 4.7 percent and the expected return on the market is 13 percent, what is the company's cost of equity capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Cost of equity capital %arrow_forward
- You were analyzing a stock and came up with the following probability distribution of the stock returns. What is the coefficient of variation on the company's stock?Round your answer to two decimal places. For example, if your answer is $345.6671 round as 345.67 and if your answer is .05718 or 5.7182% round as 5.72. State of the Economy Probability of State Occurring Stock's Expected Return Boom 20.00% 21.00% Normal 46.00% 14.60% Recession 34.00% 8.45%arrow_forwardSteady Company's stock has a beta of 0.21. If the risk-free rate is 5.9% and the market risk premium is 6.9%, what is an estimate of Steady Company's cost of equity?arrow_forwardYou were analyzing a stock and came up with the following probability distribution of the stock returns. What is the coefficient of variation on the company's stock?Round your answer to two decimal places. For example, if your answer is $345.6671 round as 345.67 and if your answer is .05718 or 5.7182% round as 5.72. State of the Economy Probability of State Occurring Stock's Expected Return Boom 20.00% 22.15% Normal 46.00% 17.35% Recession 34.00% 9.50%arrow_forward
- 2. Based on the following information calculate the expected return and standard deviation for the two stocks: State of economy Probability of state of economy Rate of return if state occur Stock A Stock B -.17 .12 .29 Recession Normal Boom 3. How should the price of a stock change when it goes ex-dividend? 4. Suppose stock in Gamma Air Freight has a beta of 1.25. the market risk premium is 7% and the risk free rate is 6%. Alpha's last dividend was $2 per share and the dividend is expected to grow at 8% indefinitely. The stock currently sells for $30. What is Gamma's cost of equity capital? .05 .65 .30 .05 .08 .13arrow_forwardIf the stocks are less risky than bonds, then the risk premium on stock may be zero. Assuming that the risk-free interest rate is 2 percent, the growth rate of dividends is 1 percent and the current level of dividends is $70, use the dividend-discount model to compute the level of the S&P 500 that is warranted by the fundamentals. Compare the result to the current S&P 500 level of 4300, and explain one possible reason for the difference.arrow_forwardSome investors use the Sharpe ratio as a way of comparing the benefits of owning shares of stock in a company to the risks. The Sharpe ratio of a stock is defined as the ratio of the difference between the mean return on the stock and the mean return on government bonds (called the risk-free rate rf ) to the SD of the returns on the stock. The mean return on government bonds is rf = 0.03% per day. The table below describes the daily return of three stocks. Date APPLE. TESLA GM 01/10/20 0.85% 4.46% 2.67% 02/10/20 -3.23% - 7.38% 0.26% 05/10/20 3.08% 2.55% 1.64% 06/10/20 -2.87% -2.75% -1.81% 07/10/20 1.70% 2.73% 4.01% 08/10/20 -0.10% 0.15% 1.87% 09/10/20 1.74% 1.90% -0.16% 12/10/20 6.35% 1.91% 0.16% 13/10/20 -2.65% 0.98% -1.06% 14/10/20 0.07% 3.28% -0.63% 15/10/20 -0.40% -2.69% 2.90% 16/10/20 -1.40% -2.05%…arrow_forward
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