The values in Table 2 are the weights of the risk-free asset and the risky assets in the optimal combined portfolio for a given holding period and risk-aversion level. The table also shows the expected return and standard deviation about that return for each portfolio. The third row of results shows that for a one-year holding period and a “middle level” of risk aversion, the optimal allocation is 82.2% in the risk-free, 10.4% in T-Bonds, 4.5% in World Bonds, 1.7% in Large Stocks and 1.2% in Small Stocks. This portfolio’s expected return is 1.42% and its standard deviation is 1.43%. Similarly the seventh row of results shows that for a five-year holding period and a “middle level” of risk aversion, the optimal allocation is 40.2% in the risk-free, 41.4% in T-Bonds, 3.2% in World Bonds, 9.0% in Large Stocks and 6.3% in Small Stocks.
Selected Answer: False Question 8 The Delphi develops a consensus forecast about what will occur in the future. Selected Answer: True Question 9 __________ is a measure of dispersion of random variable values about the expected value. Selected Answer: Standard Deviation Question 10 In Bayesian analysis, additional information is used to alter the __________ probability of the occurrence of an event. Selected Answer: Marginal Question 11 The __________ is the maximum amount a decision maker would pay for additional information. Selected Answer: Expected Value of Perfect Information Question 12 In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.
1. You are considering investing in one of the these three stocks: Stock A B C Standard Deviation 20% 10% 12% Beta 0.59 0.61 1.29 If you are a strict risk minimizer, you would choose Stock ____ if it is to be held in isolation and Stock ____ if it is to be held as part of a well-diversified portfolio. a. A; B. b. B; A. c. C; A. d. C; B. e. A; A.
Explain why. If Sharon were risk-indifferent, she would select Investments X and Y since they have higher returns than that of the 12% required return. “The attitude toward risk in which no change in return would be required for an increase in risk” (Gitman, 2009). b. If she were risk-averse, which investments would she select?
Chapter 3 Risk Identification and Measurement I. Multiple Choice 1. A listing of a random variable’s possible outcomes and the respective probabilities of those outcomes is called the: a. expected value b. standard deviation c. probability distribution d. correlation Answer: c Type: K 2. Multiplying each possible outcome of a random variable by its probability of occurrence, and then adding up these results will be equal to the random variable’s: a. expected value b. standard deviation c. probability distribution d. correlation Answer: a Type: K 3. The graph above depicts the probability distributions for risks A and B.
1. The mean, variance and standard deviation of each stock is, | |S&P 500 |Reynolds |Hasbro | |Mean |0.005743333 |0.018748333 |0.011838333 | |Variance |0.001297233 |0.008773054 |0.006586676 | |SD |0.036017126 |0.093664583 |0.081158341 | From the perspective of variance, Hasbro tends to be the most risky among the three. The higher variance indicate higher chance that the actual return on Hasbro deviate from the expected return. The reward-to-risk ratio of each individual stock is, [pic] Sharpe ratio of Reynolds = 0.138846505 Sharpe ratio of Hasbro = 0.075100106 Since Reynolds has a higher Sharpe ratio, Reynolds can yield higher return by taking the same amount of risk. The variance of a portfolio equals, [pic] |Covariance S&R |0.000938549 | |Covariance S&H |0.001811114 | To form a portfolio including the S&P 500 stocks and either of Reynolds or Hasbro, the variance of the portfolio equals, | |S&P 500 |Reynolds |Hasbro |Portfolio Variance | |Weight |0.99 |0.01 | |0.001290879 | In terms of portfolio variance, Sharpe should form the portfolio which include 0.99 of S&P 500 and 0.01 Reynolds.
Because of their risk policy and their leverage, the position has to be limited to 50%*(5%*500milllion), where the 500 million is the Green Circle’s capital base. With a position limited to $12.5 million, the maximum number of Alza’s shares they can buy is 12.5mio/48$, i.e 260’416.66 shares. Rounded, they should receive 1.2 Abbot share per Alza share, so they have to sell 260’000*1.2=312’000 shares. That’s why they short 312’000 Abott shares and are long on 260’000 Alza shares. Assuming each share of alza was bought for : if at the end of the merge, the price of Abbott share is at x $, Then for each share of Alza owned, we receive 1.2 shares of Abbott, ie in $ : Expected gain / loss 48 33.5 40.2 -7.8 48 38.5 46.2 -1.8 48 43.5 52.2 4.2 48 48.5 58.2 10.2 48 53.4 64.08 16.08 Assuming each share of abott was sold for : if at the end of the merge, the price of Abbott share is at Expected gain / loss And as there is a ratio of 1.2Abbott share per Alza share : This yield to a gross spread per share of 43.5 33.5 10 12 4.2 43.5 38.5 5 6 4.2 43.5 43.5 0 0 4.2 43.5 48.5 -5 -6 4.2 43.5 53.4 -9.9 -11.88 4.2 As we can see with the table above, with the short position the risk that Green Circle receives less than the spread in case of major price variations before the end of the merge, is deleted.
* Risk premium: Arithmetic mean is often used for one-year period valuation, while geometric mean is better for long-term period estimated expected returns. * Beta: Cohen took the average value of historical betas to measure the risk. From my perspective, however, the most recent beta is more representative than the average beta in terms of reflecting future risk. Question 2: What is your estimate of the equity cost of capital? Based on the analysis in question 1, I estimate the cost of equity as following: 9.81% =5.74% + 0.69 * (5.9%) Question 3: How, if at all, would you change Cohen’s debt cost of capital calculation?
What is ABCs expected share price post exercise of warrants? What is the yield on ABCs bonds with warrants? Solution: The price of ABC’s straight bond at time of issuance is B= 1, 000 + $50 $50 $50 + ... + + 2 1 + 10% (1 + 10%) (1 + 10%)20 1 − (1 + 10%)−20 $1, 000 = $50 × + 10% (1 + 10%)20 = $574.32 The value of a warrant at time of issuance is W = $1, 000 − $574.32 = $21.28
YTM call = YTM non callable + risk premium Determined by ability of being called, and how much of risk. It would cost to create the synthetic bond $ 98.783. Ask ( Price at which Issuer / Dealer is willing to sell the bond for. Bid ( Price at which Issuer/Dealer is willing to buy the bond. | | | | | | | | | |Treasury Bonds | | | | | | | | |Ask |Bid |Coupon | | | |81/4 May 00-05 |101.25 |101.125 |4.125 | | | |12-May-05 | |129.9063 |129.7188 |6 | | | |8 7/8 May 00 |104.5 |104.375 |4.4375 | | | | | | | | | | | |STRIPS | | | | | | | | | | | |