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Investment Analysis & Portfolio Management

Sharpe’s Single Index Model

Practice Sheet -2

| |1. Betas of two stocks are 0.73 and 1.20 respectively. If the standard deviation of the market returns is 15.49%, the covariance between | |
| |the two stock’s return is | |
| |(a) 175.20(%)2 (b) 210.20(%)2 (c) 288.20(%)2 (d) 328.76(%)2 (e) 345.60(%) | |
| | | |
| |2. The index model for two stocks A and B is estimated as follows: | |
| |RA = 2% + 0.65RM + eA , RB= 4% + 1.10RM + eB | |
| |[pic] =25% | |
| |(2 A = 0.15 and (2B = 0.30 (in relation to return on the market index) | |
| |(The symbols are in standard notation) | |
| |The correlation coefficient between the returns on two stocks is | |
| |a. 0.12 b. 0.21 c. 0.35 d. 0.79 e. 0.92. | |
| | | |
| |3. A portfolio management organization analyzes 75 stocks and constructs a mean-variance efficient portfolio that is constrained to these | |
| |75 stocks. How many estimates of expected returns, variances and covariances are needed to optimize this portfolio? (Using Sharpe’s Model)| |
| | | |
| |4. Mr. Ramesh Mittal has gathered the following information relating to six stocks: (U = E(r) – ((i2 /tk)) | |
| | | |
| |Stock | |
| |Alpha (%) | |
| |Unsystematic risk (%)2 | |
| |Total Risk (%)2 | |
| | | |
| |HUL | |
| |2.20 | |
| |55 | |
| |95 | |
| | | |
| |Tata Steel | |
| |1.20 | |
| |36 | |
| |80 | |
| | | |
| |NIIT | |
| |1.10 | |
| |20 | |
| |65 | |
| | | |
| |Tech Mahindra | |
| |1.35 | |
| |15 | |
| |40 | |
| | | |
| |Bajaj Auto | |
| |0.90 | |
| |12 | |
| |35 | |
| | | |
| |ACC | |
| |0.65 | |
| |15 | |
| |45 | |
| | | |
| |The risk free rate is 5%, return on the market index is 12% and the variance of the return on the index is 25 (%)2. You are required to | |
| |a. Construct a portfolio using Sharpe’s portfolio optimization model. | |
| |b. Verify whether the stocks selected in optimum portfolio have higher utility than the rejected stocks, if the risk tolerance of Mr. | |
| |Mittal is 40%. | |
| | | |
| |5. Mr. Deepak Patnaik has gathered the following information relating to six stocks. | |
| |Stock | |
| |Alpha (%) | |
| |Unsystematic risk (%) 2 | |
| |Total Risk (%)2 | |
| | | |
| |ACC | |
| |2.10 | |
| |45 | |
| |75 | |
| | | |
| |Procter & Gamble | |
| |1.25 | |
| |15 | |
| |40 | |
| | | |
| |Ranbaxy | |
| |1.30 | |
| |14 | |
| |42 | |
| | | |
| |ICICI | |
| |1.45 | |
| |20 | |
| |55 | |
| | | |
| |MRF | |
| |0.95 | |
| |14 | |
| |32 | |
| | | |
| |Wipro | |
| |0.82 | |
| |16 | |
| |35 | |
| | | |
| |The risk free rate is 7%, return on the market index is 12% and variance of the return on the index is 25%2. | |
| |a. Construct a portfolio using Sharpe’s portfolio optimization model. | |
| |b. Verify whether the stocks selected in optimum portfolio have higher utility than the rejected stocks, if the risk tolerance of Mr. | |
| |Deepak Patnaik is 40%, | |
| |6. Mr. Atul Sharma has forecasted that the market return follows the following relationship | |
| |Rm = Risk free rate + Risk premium of 7%. | |
| |Variance on market is 25%2 | |
| |He has zeroed in on the following stocks with the parameters given below: | |
| |Stock | |
| |Alpha (%) | |
| |Beta | |
| |Residual Variance (%)2 | |
| | | |
| |A | |
| |1.50 | |
| |0.95 | |
| |9.25 | |
| | | |
| |B | |
| |0.75 | |
| |0.97 | |
| |5.95 | |
| | | |
| |C | |
| |0.45 | |
| |1.25 | |
| |9.75 | |
| | | |
| |D | |
| |1.35 | |
| |1.05 | |
| |5.35 | |
| | | |
| |E | |
| |0.95 | |
| |1.10 | |
| |4.50 | |
| | | |
| |The risk-free rate is 5% p.a. | |
| |Construct an optimum portfolio using the Sharpe’s optimization method. | |
| | | |
| |7. | |
| |Stock | |
| |Alpha (%) | |
| |Beta | |
| | | |
| |Tata Steel | |
| |-2.06 | |
| |0.5 | |
| | | |
| |Tata Tea | |
| |-1.5 | |
| |0.92 | |
| | | |
| |Bajaj Auto | |
| |1.15 | |
| |0.58 | |
| | | |
| |ITC | |
| |1.45 | |
| |1.15 | |
| | | |
| |If market return is 15%, find the portfolio return for an investor who invests equal amount of money in the above stocks | |
| |8. Mr John is advised by a friend to buy the following stocks in equal proportion : | |
| |Stock | |
| |Beta | |
| |Residual Variance | |
| | | |
| |A | |
| |0.84 | |
| |0.5 | |
| | | |
| |B | |
| |1.27 | |
| |0.92 | |
| | | |
| |C | |
| |1.17 | |
| |0.58 | |
| | | |
| |The market return variance is 25 % 2 . Find the portfolio risk. | |
| | | |
| | | |
| |9. The following table shows the data for some stocks. Which stock has the highest unique risk? | |
| |Stock | |
| |Variance | |
| |r | |
| | | |
| |1 | |
| |6.3 | |
| |0.42 | |
| | | |
| |2 | |
| |9 | |
| |0.2 | |
| | | |
| |3 | |
| |8.64 | |
| |0.18 | |
| | | |
| |4 | |
| |9.12 | |
| |0.21 | |
| | | |
| |5 | |
| |5.86 | |
| |0.19 | |
| | | |
| |Market | |
| |2.69 | |
| | | |
| | | |
| | | |
| |10. Vinay received Rs 10 lacs from his pension fund. He wants to invest in the stock market. The T bill rate is 5% and market return | |
| |variance is 10%2. The following table gives the details regarding various stock, Construct optimal portfolio using Sharpe’s model. | |
| |Stock | |
| |Expected Return | |
| |Beta | |
| |Residual Variance | |
| | | |
| |A | |
| |15 | |
| |1 | |
| |30 | |
| | | |
| |B | |
| |12 | |
| |1.5 | |
| |20 | |
| | | |
| |C | |
| |11 | |
| |2 | |
| |40 | |
| | | |
| |D | |
| |8 | |
| |0.8 | |
| |10 | |
| | | |
| |E | |
| |9 | |
| |1 | |
| |20 | |
| | | |
| |F | |
| |14 | |
| |1.5 | |
| |10 | |
| | | |
| | | |
| |11. The following table gives data on four stock: | |
| |Stock | |
| |Alpha | |
| |Systematic Variance | |
| |Unsystematic Variance | |
| | | |
| |A | |
| |-0.06 | |
| |5 | |
| |4 | |
| | | |
| |B | |
| |0.1 | |
| |2 | |
| |6 | |
| | | |
| |C | |
| |0 | |
| |3 | |
| |1 | |
| | | |
| |D | |
| |-0.14 | |
| |3 | |
| |2 | |
| | | |
| |The market is expected to have a 12% return with a return variance of 6%2. Calculate the expected return for a portfolio assuming equal | |
| |proportion of each of the stock. | |
| |11. The following table gives data on four stocks : | |
| | | |
| |Stock | |
| |Alpha | |
| |Systematic Variance | |
| |Unsystematic Variance | |
| | | |
| |A | |
| |-0.06 | |
| |5 | |
| |4 | |
| | | |
| |B | |
| |0.1 | |
| |2 | |
| |6 | |
| | | |
| |C | |
| |0 | |
| |3 | |
| |1 | |
| | | |
| |D | |
| |-0.14 | |
| |3 | |
| |2 | |
| | | |
| |The market is expected to have a 12% return over a forward period with a return variance of 6% . Calculate the expected return for a | |
| |portfolio consisting of equal portion of all the four stocks. | |
| |12. | |
| |Stock | |
| |Alpha | |
| |Beta | |
| |Unsystematic Risk | |
| | | |
| |ABC | |
| |-0.05 | |
| |1.6 | |
| |0.04 | |
| | | |
| |RSE | |
| |0.08 | |
| |-0.3 | |
| |0 | |
| | | |
| |GIV | |
| |0 | |
| |1.1 | |
| |0.1 | |
| | | |
| |If the market index is expected to have a return of .2 and a variance of .2 which single stock would the investor prefer to own from a risk| |
| |and return point of view? Interpret the value of both unsystematic risk and alpha value of all the three stocks. | |