MN-1504 Seminar Eight (with solutions) PDF

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Seminar Questions and Solutions for Accounting and Finance for Economics...

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MN-1504

Accounting and Finance for Economics (Seminar Eight)

Question One Stock Y has a beta of 1.59 and an expected return of 25%. Stock Z has a beta of 0.44 and an expected return of 12%. If the risk-free rate is 6% and the market risk premium is 11.3%, are these stocks correctly priced? Based on the CAPM, we know (𝑅𝑖)=𝑅𝑓+𝛽𝑖×[𝐸(𝑅𝑚)−𝑅𝑓)] , so we get E(Ry)=6%+1.59*11.3%=23.97%, E(Rz)=6%+0.44*11.3%=10.97% Since the expected return from investors is 25% for asset Y, which is actually priced at 23.97% by the CAPM, CAPM undervalues the asset price while such asset is overvalued (two sides of one coin). Since the expected return from investors is 12% for stock Z, which is actually priced at 10.97% by the CAPM, so again, the asset is overvalued. As a current investor in the stock market, you should sell all those overvalued securities.

Question Two Calculate the expected return, variance, and standard deviations for investments in either stock A or stock B, or an equally weighted portfolio of both. Scenario

Probability

Return on A

Return on B

Recession Normal

25% 40%

-4% 8%

9% 4%

Boom

35%

20%

-4%

Stock A: Expected return = (.25u-4%) + (.40u8%) + (.35u20%) = 9.2% Variance = .25(-4% - 9.2%)2+ .4(8%- 9.2%)2 + .35(20%- 9.2%)2 = 43.56 + .58 + 40.82 = 84.96 ; Standard deviation = (84.92)^(0.5) = 9.22% Stock B: Expected return = (.25u9%) + (.40u4%) + (.35u-4%) = 2.45% Variance = .25(9% - 2.45%)2 + .4(4% - 2.45%)2 + .35(-4% - 2.45%)2 = 10.73 + .96 + 14.56 = 26.25; Standard deviation = (26.25)^(0.5) = 5.12% Portfolio: Expected return = (.5u9.2%) + (.5u2.45%) = 5.83% Variance = .25(((-4% + 9%) u0.5) - 5.83%)2+ .4(((8% + 4%)u0.5) - 5.83%)2 + .35 ((20% 4%)u0.5) - 5.83%)2 = 2.77 + .01 + 1.65 = 4.43; Standard deviation = 4.43^(0.5) = 2.1% 1

Note that the standard deviation of the portfolio is considerably less than that of either Stock A or Stock B.

Question Three Calculate the nominal return, real return, and risk premium for the following common stock investment: Purchase price

$60 per share

Dividend Sales price

$3.5 per year $73 per share

Treasury bill yield Inflation rate

8.50% 7.50%

Solutions:

Question Four Discuss the statement, "Only market risk matters to a diversified investor." 2

It is relatively easy for an investor to diversify a portfolio sufficiently to the point where nearly all of the remaining risk is market risk. This can be achieved by combining somewhere between 15 and 20 different securities. At that point, then, the investor does not care about a strike at General Motors because that element of unique risk has been offset by a boom in the semiconductor industry. Any investor who chooses not to diversify and thus retain the unique risk should be prepared to suffer the consequences; basically, risk level will increase without a corresponding increase in expected yield. These statements should show that diversified investors are concerned only with the market risk in their portfolios, rather than any elements of unique risk.

Question Five Explain the concepts of unique risk and market risk, and how the total level of portfolio risk can change by adding additional securities. Unique or diversifiable risks apply specifically the firm in question—for example, risk due to changing input prices or changing demand or renegotiation of labor contracts, and so on. While these (and numerous other) examples of unique risk can dramatically affect returns on the firm's stock, these types of risk can be diversified away by combining stocks that do not move in lock-step fashion into a portfolio. Then, for example, the increase in steel prices is balanced with a decrease in wheat prices to even out the ups and downs of investing in individual stocks. Although few stocks move in perfect harmony, most move in the same direction, or are said to be positively correlated. It can be especially beneficial for risk reduction to add to the portfolio those few stocks that are expected to have a negative correlation. While most diversification is risk-reducing, adding negatively correlated stocks can have the largest amount of risk reduction. On the other hand, market risks are felt by all firms (although not necessarily to the same extent) and thus cannot be diversified away. Examples of these systematic, or macro, risks would be interest rates, business cycles, exchange rates, and so forth. Adding securities to a portfolio will mitigate the unique risk, and total risk will thus approach the level of market risk after 15 or 20 securities are combined. Beyond that degree of diversification, few benefits in the form of risk reduction are actually received.

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