Part 1: Short Answer Questions (12 questions in total)
$45,000/(1-50%)/$150 = 600 shares
($20 – $25)*100 = -$500
Answer: Future dividends (including the dividend growth rate) and the discount rate
Answer: 50%*60% = 30%______________________________
Answer: a concentrated ownership means a small number of large shareholders will have control over the firm. They can make suboptimal decisions to benefit themselves (like in a pyramidal structure) and hurt minority shareholders.
Answer: _i
Answer: taking more risk; insider trading; technical analysis; front-running on public information;
Answer: Diversification is the practice of having multiple assets, ideally assets with low correlations, in a portfolio. Diversification can effectively reduce portfolio risk without necessarily lowering portfolio expected return.
Answer: any two of disposition effect (prospect theory), overconfidence, attention affect, memory bias, conservatism, home bias, and so on.
Part 2: Comprehensive Word Problems (2 problems in total)
Please show your steps to get partial credit.
Problem 1
A mutual fund has three assets in its portfolio: Stock A, Stock B and the risk-free asset. Stock A has a beta of 3 and Stock B has a beta of 1.5. The risk-free asset has an expected return of 1%. The expected market return is 12%.
12% – 1% = 11%
Use CAPM: E(rA) = 1% + 3*(12%-1%) = 34% > 30% è overpriced è short (sell);
E(rB) = 1% + 1.5*(12%-1%) = 17.5% <20% è underpriced è long (buy)
Beta = 30%*3 + 35%*1.5 + 35%*0 = 1.425
CAPM: E(rp) = 1% + 1.425*(12%-1%) = 16.675%
Problem 2
In a simple economy, there are three economic states: good, normal and bad. A hedge fund invests in two stocks: Cats Company and Dogs Company. Stock returns of the two stocks in each economic state is given in the table below (Table 1). The risk-free rate is 1%.
Table 1: Stock Returns in Different Economic States | |||
Probability | Cats Co. | Dogs Co. | |
Good | 25% | 25% | 12% |
Normal | 40% | 5% | 0% |
Bad | 35% | -10% | 5% |
E(r_cats) = 25%*25%+40%*5%+35%*(-10%) = 4.75%
E(r_dogs) = 25%*12%+40%*0%+35%*5% = 4.75%
Stock Cats: Var = 25%*(25%-4.75%)^2 + 40%*(5%-4.75%)^2 + 35%*(-10%-4.75%)^2 = 1.7869% %; Std Dev = 13.37%
Stock Dogs: Var = 25%*(12%-4.75%)^2 + 40%*(0%-4.75%)^2 + 35%*(5%-4.75%)^2 = 0.2219%; Std Dev = 4.71% è Stock Cats has a higher standard deviation.
Because Cats and Dogs have the same expected return but Cats has a higher standard deviation, Dogs has a higher Sharpe Ratio.
Sharpe ratio:
Cats: (4.75%-1%)/13.37% = 28.05%
Dogs: (4.75%-1%)/4.71% = 79.61%
Weights = 40% for cats and 60% for dogs; Portfolio return in the good, normal and bad states are 17.2%, 2% and -1%, respectively.
E(rp) = 17.2%*25%+2%*40%+-1%*35% = 4.75%
Var(portfolio) = 25%*(17.2%-4.75%)^2 + 40%*(2%-4.75%)^2 + 35%*(-1%-4.75%)^2 = 0.5335%
Std. Var. of portfolio = 7.30%; Sharpe ratio = (4.75%-1%)/7.3% = 0.514
The portfolio is better than cats but not better than dogs.
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