Corpfin Mod 7: Homework


Corpfin Mod 7: Homework

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NEAS
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Corporate Finance, Module 7, “Risk and Return”

Corporate finance module 7: Readings for Eleventh Edition

(The attached PDF file has better formatting.)

The page numbers here are for the eleventh edition of Brealey and Myers. You may also use the seventh, eighth, ninth, or tenth editions of this text. The page numbers for earlier editions are in separate postings. The substantive changes in the textbook are slight among these editions, but the final exam problems are based on the eleventh edition.

{The Brealey and Myers textbook is excellent. We say to read certain sections and to skip others. This does not mean that certain sections are better; it means that the homework assignments and exam problems are based on the sections that you must read for this course. Some of the skipped sections are fascinating, but they are not tested.}

The introduction on page 190 summarizes the key concepts. We differentiate between unique risk, which is diversifiable, and market risk, which is not diversifiable.

The Capital Asset Pricing Model (CAPM) posits that the excess return of a project is proportional to its beta.

●    The excess return is the return minus the risk-free rate.
●    The beta is the covariance of the security’s return (or project’s return) with the market return divided by the variance of the market return.

Modern portfolio theory says that systematic risk warrants a higher return. The CAPM says what the higher return should be for each security.

Read section 8.1 on pages 190-197, which reviews modern portfolio theory. Brealey & Myers give a summary so that they can discuss corporate financing (equity vs debt). They are teaching how to structure a company, not how to structure an investment portfolio. But the two subjects are intertwined, so they must review modern portfolio theory.

Focus on the section “we introduce borrowing and lending” on pages 195-197; know the Sharpe ratio at the bottom of page 196. The Sharpe ratio is often tested on the final exam.

Read section 8.2, “the relation between risk and return,” on pages 197-200. Know the meaning of the security market line (Figure 8.7 on page 200) and the formula for the expected risk premium for common stocks on page 200. The review of the CAPM on page 199 is good, and the subsection on pages 199-200 (“What if a stock did not lie on the security market line?”) is essential for the theory.

Section 8.3 is optional. Although the theory is good, the CAPM hasn’t fared well from empirical testing (though it has done better than anything else). The final exam does not test this section, and no homework assignments are drawn from it. But after reading about the CAPM, it is worthwhile hearing the cautions against adopting it uncritically.

From section 8.4 (pages 204-208), skip the parts on the consumption beta and arbitrage pricing theory are for theorists; you may never use them in your work careers. Read the part on the three factor model (pages 206-208); this model is now commonly used.

Question: I have heard that the CAPM is not supported by the evidence, and the consumption CAPM, behavioral finance, and arbitrage pricing theory better explain stock returns.

Answer: It is true that the CAPM has not fared as well in empirical research as we had once expected it would. But the competing theories mentioned above don’t even suggest how to price stocks. The arbitrage pricing theory says that several factors explain stock returns, not just the covariance with market returns. But it doesn’t even tell us what these other factors are; we can’t use the theory to explain stock returns and we can’t test the theory. Behavioral finance suggests that investors are not perfectly rational, but it is vague about how investors make decisions. It discusses many qualitative items that may indeed have an effect. But it does not suggest how to quantify the effects, so we can’t use it to price stocks and we can’t even test the theory.

The Fama/French three factor model is now commonly used for insurance pricing and fair values of unpaid losses. You will deal with both the CAPM and the Fama/French model in your actuarial careers, though this course focuses on the CAPM.

Read the summary on pages 208-209.

Review problems 9 and 11a on page 212, and problem #16 on page 213.

Skip the mini-case on pages 216-217.

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CorpFinance.Module7.HW.pdf (946 views, 52.00 KB)
Edited 6 Years Ago by NEAS
ugastat06
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Question about 7.2

When I am finding the market risk premium, I subtracted the following two equations:

.16 = rf + .8(rm - rf)
.23 = rf + 1.5(rm - rf)

-.07 = -.7(rm -rf)

Therefore, is the risk premium 1%?

Also, I when I plugged in .01 for (rm - rf), I ended up getting different rf's, which I know shouldn't occur. Any advice as to what I may be doing wrong?

[NEAS: 10%, not 1%; check the decimal place.]


skibum
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Here is what I did for 7.2:  Use the formula they describe in the problem, which is

(rm-rf) x (beta1- beta2) = r1-r2

Plug in given values to solve for rm-rf  Then use r = rf + beta x (rm-rf) with one set of the given data to solve for rf

I kept getting an answer for rf that did not work also then realized I was using .08 not .8 as the given beta value. 


jar52
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For question 7.3 part G, would you like us to label the best and worst portfolio out of the three portfolios listed, or would you also like us to include combinations of those portfolios when deciding the best and the worst.

[NEAS: Label the best and worst and explain why.]


JJ
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I dont understand how to calculate 7.3(a). How to calculate the beta portfolio? Is it just solving the equation of .12y + 0.16(1-y) = .2? It will come down to y=-1. So the combined beta portfolio is -1?

[NEAS: The investor forms a combined portfolio with Z% of portfolio 1 and (1 – Z%) of portfolio 2. The problem says that Z% × 12% + (1 – Z%) × 16% = 20% –4% × Z% = 4% Z% = –1. An investor who buys 2 of portfolio 2 and sell short 1 of portfolio 1 get a combined return of 2 × 16% – 1 × 12% = 20%. Now work out the beta of the combined portfolio.]


Edited 11 Years Ago by NEAS
NEAS
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JJ - 7/14/2011 4:37:09 PM
I dont understand how to calculate 7.3(a). How to calculate the beta portfolio? Is it just solving the equation of .12y + 0.16(1-y) = .2? It will come down to y=-1. So the combined beta portfolio is -1?

[NEAS: The investor forms a combined portfolio with Z% of portfolio 1 and (1 – Z%) of portfolio 2. The problem says that Z% × 12% + (1 – Z%) × 16% = 20% –4% × Z% = 4% Z% = –1. An investor who buys 2 of portfolio 2 and sell short 1 of portfolio 1 get a combined return of 2 × 16% – 1 × 12% = 20%. Now work out the beta of the combined portfolio.]


 

Nate E
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When it comes to 7.3 G, it seems pretty straightforward to determine that portfolio #2 is the best. If you assign 50% to portfolio #1 and 50% to portfolio #3, you get an expected return of 16% and a beta of 1.25, versus an expected return of 16% and a beta of 1.1 with 100% allocation in portfolio #2. The actual has a lower beta than the synthetic at the same expected return. Alternately, we could assign 60% to portfolio #1 and 40% to portfolio #3, which would give us a beta of 1.1 and an expected return of 15.2%. That is, at an equivalent beta the actual generates higher returns than the synthetic. It follows that portfolio #2 is better than both of the portfolios combining to form the synthetic.

W‌ith that said, how is it possible to determine whether portfolio #1 or #3 is worse?‌ Doesn't it depend entirely on subjective risk preferences? Thanks!
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Nate E - 9/11/2022 6:34:56 AM
When it comes to 7.3 G, it seems pretty straightforward to determine that portfolio #2 is the best. If you assign 50% to portfolio #1 and 50% to portfolio #3, you get an expected return of 16% and a beta of 1.25, versus an expected return of 16% and a beta of 1.1 with 100% allocation in portfolio #2. The actual has a lower beta than the synthetic at the same expected return. Alternately, we could assign 60% to portfolio #1 and 40% to portfolio #3, which would give us a beta of 1.1 and an expected return of 15.2%. That is, at an equivalent beta the actual generates higher returns than the synthetic. It follows that portfolio #2 is better than both of the portfolios combining to form the synthetic.

W‌ith that said, how is it possible to determine whether portfolio #1 or #3 is worse?‌ Doesn't it depend entirely on subjective risk preferences? Thanks!


Yes, we cannot definitely say which portfolio is the worst of the three, though we can say that a portfolio is better or worse than a combination of the other two.
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