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Chapter 7 Solutions
Derivatives and Risk Management (Options, Futures and Derivatives)
SVKM's NMIMS
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Solutions to Chapter 7 Textbook Problems 1.
Expected payoff = (.10 × 500) + (.50 × 100) + (.40 × 0) = 100 Rates of return: (500 – 100) / 100 = 400% (100 – 100) / 100 = 0% (0 – 100) / 100 = –100% Expected rate of return = (.10 × 400%) + (.50 × 0%) + (.40 × –100%) = 0% Variance = .10(400% – 0)^2 + .50(0% – 0)^2 + .40(–100% – 0)^2 = 20, Standard deviation = 20,000^0 = 141% 4
a. False. Investors prefer diversified portfolios because diversification reduces variability and therefore reduces risk. However, the diversification of an individual company does not necessarily make it less risky. b. True. Stocks must be less than perfectly positively correlated in order to obtain diversification benefits. c. False. The risk eliminated by diversification is called specific risk, or the risk surrounding an individual company or industry. Market risk will still exist in a fully diversified portfolio. d. False. It is true that the greatest benefit to diversification occurs when stocks are uncorrelated. However, most stocks tend to move in the same direction. There are still benefits to diversification any time stocks are less than perfectly positively correlated. e. False. The contribution to portfolio risk depends on the relationship of the stock to the market as a whole. f. True. Market risk is the risk that relates to a diversified portfolio. g. True. The only risk inherent in a diversified portfolio is market risk. h. False. An undiversified portfolio with a beta of 2 is twice as risky as the market portfolio. Part of that risk will be market risk and part will be specific risk. 5.
βp = {(5 × 1) + [(10 – 5) × 1)]} / 10
βp = 1.
Beta measures systematic risk which cannot be eliminated by diversification.
The beta of each stock is given by the slope of the line, or the rise divided by the run. The run is the range of the market returns while the rise is the range of the stock returns.
BetaA = (0 – 20) / (– 10 – 10) = 1
BetaB = (– 20 – 20) / (– 10 – 10) = 2
BetaC = (– 30 – 0) / (– 10 – 10) = 1.
BetaD = (15 – 15) / (– 10 – 10) = 0
BetaE = (10 – (–10) / (– 10 – 10) = – 1
In the context of a well-diversified portfolio, the only risk characteristic of a single security that matters is the security’s contribution to the overall portfolio risk. This contribution is measured by beta. Lonesome Gulch is the safer investment for a diversified investor because its beta of. is lower than the beta of Amalgamated Copper of .66. For a diversified investor, the standard deviations are irrelevant.
a. σ P 2 = .60 2 × .10 2 + .40 2 × .20 2 + 2(.60 × .40 × 1 × .10 × .20) σP 2 =. b. σP 2 = .60 2 × .10 2 + .40 2 × .20 2 + 2(.60 × .40 × .50 × .10 × .20) σP 2 =. c. σP 2 = .60 2 × .10 2 + .40 2 × .20 2 + 2(.60 × .40 × 0 × .10 × .20) σP 2 =.
Chapter 7 Solutions
Course: Derivatives and Risk Management (Options, Futures and Derivatives)
University: SVKM's NMIMS
