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theory of corporate finance

Questions and Answers of Theory Of Corporate Finance

Two risky portfolios with a correlation of −1 can be combined into an asset that has no risk. Thus, its expected rate of return has to be the same as that on the risk-free asset—or you could get
The mean rate of return for portfolio (wH= 0.1, wI= 0.9) is 0.1 . 6% + 0.9 . 9% = 8.7%. You can also compute this from the rates of return in the 4 states −11.4%, 17.4%, 21.6%, and 7.2%. Demeaned,
This is an important question. In fact, you should memorize Formula 8.15 that describes how risk grows over time. The assumption that there is no compounding (that you can ignore the cross-product)
The covariance between H and I is 45%% (Formula 8.9). The variance of H is 90%%, the variance of I is 189%% (Table 8.4). Therefore, the shortcut Formula 8.10 gives Var(˜rM) = (3/4)2 . 90%% + (1/4)2
For M, the covariance between H and I was computed as 45%% in Formula 8.9. The variance of H is 90%% (from Table 8.4 on page 232), the variance of I is 189%% (from the same figure). Therefore, using
The portfolio variance of portfolio N in Table 8.4 is Sdv(TH) = Var(TH) = = 22 (-7.5% -6.75%)2 + (13.5% 6.75%) 2 + (6% 6.75%) 2 + (15% 6.75%) 4 203.0625 %% + 45.5625% % +0.5625 %% + 68.0625%% 4
The rates of return of portfolioMin Table 8.4 are−8% (♣), +14% (♦), 8% (♥), and 14% (♠). The deviations from the mean are −15%, 7%, 1%, and 7%.When squared, they are 225%%, 49%%, 1%%, and
Would the tangency portfolio invest in more or less H if the risk-free rate were 3% instead of 4%? (Hint: Think visually.)
Formula 8.11 noted that the minimum-variance portfolio without a risk-free asset invests about 76.2% in H and about 24.8% in I. (Work with the rounded numbers to make your life easier.) With the
Compute the covariance of H and F.
What kind of portfolios are the points to the right of H on the line itself in Figure 8.7?
Draw the efficient frontier for the following two base assets, H and Z:Also, compute the covariance between H and Z. Is it higher or lower than what you computed in the text for H and I? How does the
If H and I were more correlated, what would the efficient frontier between them look like? If H and I were less (or more negatively) correlated, what would the efficient frontier between them look
If there are two risky portfolios that have a correlation of −1with positive investment weights, what would the expected rate of return on this portfolio be?
Compute the risk and reward of the portfolio wH= 0.1, wI= 0.9, as in Table 8.4 on page 232. Confirm that this portfolio is drawn correctly in Figure 8.5.
(This question is very important. Please do not pass over it.) Let’s consider a stock market index, such as the S&P 500. It had a historical average rate of return of about 12% per annum, and a
Show that the shortcut Formula 8.10 works for portfolio N, in which H is 3/4. That is, does it give the same 79.3%% noted in Table 8.4?
Show that the shortcut Formula 8.10 works for portfolio M, in which H is 2/3. That is, does it give the same 81.0%% noted in Table 8.4 on page 232?
Confirm the portfolio variance and standard deviation if you invest in portfolio N (wH= 3/4) in Table 8.4.
Confirm the portfolio variance and standard deviation if you invest in portfolio M (wH= 2/3) in Table 8.4.
Why do some statistical packages estimate covariances differently (and different from those we computed in this chapter)? Does the same problem also apply to expected rates of return (means) and
Are historical covariances or means more trustworthy as estimators of the future?
Download 5 years of historical monthly(dividend-adjusted) prices for Coca-Cola (KO)and the S&P 500 from Yahoo! Finance.(a) Compute the monthly rates of return.(b) Compute the average rate of return
Download the historical prices for the S&P 500 index (~spx or ~gspc) and for VPACX (the Vanguard Pacific Stock Index mutual fund)from Yahoo! Finance, beginning January 1, 2004, and ending December 31
The following represents the probability distribution for the rates of return for next month:Probability Pfio P Market M 1/6 −20% −5%2/6 −5% +5%2/6 +10% 0%1/6 +50% +10%Compute by hand (and show
Compute the expected rates of return and the portfolio betas for many possible portfolio combinations (i.e., different weights) of C and D from Table 8.1 on page 202. (Your weight in D is 1 minus
Consider the following assets:Scenario Bad Okay Good Market M −5% 5% 15%Asset X −2% −3% 25%Asset Y −4% −6% 30%(a) Compute the market betas for assets X and Y.(b) Compute the correlations of
Go to Yahoo! Finance. Obtain 2 years’worth of weekly rates of return for PepsiCo and for the S&P 500 index. Use a spreadsheet to compute PepsiCo’s market beta.
You estimate your project to return −20% if the stock market returns −10%, and +5% if the stock market returns +10%. What would you use as the market beta estimate for your project?
Look up the market betas of the companies in Table 8.2. Have they changed dramatically sinceMay 2008, or have they remained reasonably stable?
Is it wise to rely on historical statistical distributions as our guide to the future?
Why is it so common to use historical financial data to estimate future market betas?
Assume you have invested half of your wealth in a risk-free asset and half in a risky portfolio P. Is it theoretically possible to lower your portfolio risk if you move your risk-free asset holdings
Consider the following five assets, which have rates of return in six equally likely possible scenarios:Scenarios Awful Poor Med. Okay Good Great Asset P1 –2% 0% 2% 4% 6% 10%Asset P2 –1% 2% 2% 2%
What are the risk and reward of a combination portfolio that invests 40% in A and 60% in B?
Compute the value-weighted average of 1/3 of the standard deviation of C and 2/3 of the standard deviation of D. Is it the same as the standard deviation of a CDD portfolio of 1/3 C and 2/3 D, in
The following were the closing year-end prices of the Japanese stock market index, the Nikkei-225:1984 11,474 1992 16,925 2000 13,786 1985 13,011 1993 17,417 2001 10,335 1986 18,821 1994 19,723 2002
Multiply each rate of return for A by 2.0.This portfolio offers −2%, +4%, +8%, and+22%. Compute the expected rate of return and standard deviation of this new portfolio.How do they compare to those
For a firm whose debt is risk free, the overall firm beta is βFirm= 0.5 . βEquity+ 0.5 . βDebt. Thus, 0.5 . βEquity+ 0.5 . 0 = 2. Solve for βEquity= βFirm/0.5 = 4. For the (90%, 10%) case, the
The CCD portfolio has rates of return of 3.3333%, 4.00%, 4.6667%, and 4.00% in the four states. Demeaned, this is −0.6667%, 0%, 0.6667%, and 0%. Therefore, the variance of CCD is [(−0.6667%)2
To confirm that you cannot value-weight variances (and thus standard deviations):(a) The variance of ˜rC was 26.5%%. The variance of ˜rD was 90.0%%. The value-weighted average of one part variance
To check that Formula 8.6 on page 220 is correct, youmust compute the market beta for CDD from the rates of return for the entire firm CDD.(a) The second and third columns in the following table show
Using the same formula, the market beta is [(+5%) − (−5%)]/[(−10% − (+10%)]= −0.5.
The market beta of this project is(This is not “half as volatile” because market beta is not a measure of volatility.) Tx,2 - Tx,1 (-5%) (+5%) Px.M +0.5 TM,2 - FM,1 (-10%) - (+10%)
The order of subscripts on market beta is important. Algebraically, βC,M= [cov(˜rC, ˜rM)]/[var(˜rM)], whileβMC= [cov(˜rC, ˜rM)]/[var(˜rC)]. The denominator is different. The easiest way to
For the MC portfolio, the portfolio combination rates of return in the four scenarios were on the right side of the table in Figure 8.3 on page 210. Let’s confirm them first:The variance is VarMD =
For the combination portfolio of 90% in A and 10% in B:(a) The reward, that is, the expected rate of return, is 0.9 . 4% + 0.1 . 4% = 4%. To work out the variance, first compute the rates of return
The reward of portfolio C is its expected rate of return. This is simply [(−2%) + 3% + 7% + 12%]/4 =5%. (We just divide by 4, rather than multiply each term by 1/4, because all outcomes are equally
The mean of portfolio A was 4%. Adding 5% to each return will give you a mean of 9%, which is 5% higher.The variance and standard deviation remain at the same level, the latter being 4.42%. If you
The average deviation from the mean is always 0.
Assume that a firm will always have enough money to pay off its bonds, so the beta of its bonds is 0. (Being risk free, the rate of return on the bonds is obviously independent of the rate of return
Consider an investment of 2/3 in C and 1/3 in D. Call this new portfolio CCD. Compute the variance, standard deviation, and market beta of CCD. Do this two ways: first from the four individual
Let’s confirm that you cannot take a value-weighted average of component variances (and thus of standard deviations) the same way that you can take value-weighted average expected rates of return
Let’s check that the beta combination formula (Formula 8.6 on page 220) is correct. Let me lead you along:(a) Write down a table with the rate of return on the market and on portfolio CDD in each
You estimate your project to return +5% if the stock market returns−10%, and −5% if the stock market returns +10%. What would you use as the market beta estimate for your project?
You estimate your project x to return −5% if the stock market returns−10%, and +5% if the stock market returns +10%. What would you use as the market beta estimate for your project?
Return to your computation of market beta of 1.128 in Formula 8.5.We called it βC,M, or βC for short. Is the order of the subscripts important?That is, please compute βM,C and see whether it is
Confirmthe risk and reward calculations for theMC andMDportfolios in the table under Figure 8.3.
A combination portfolio named AB invests 90% in A and 10% in B.(a) Compute its risk and reward.(b) In a bar plot similar to those in Figure 8.1, would this new AB portfolio look less spread out than
Compute the risk and reward of C from Table 8.1.
Asset A from Table 8.1 offers −1%, +2%, +4%, and +11% with equal probabilities. Now add 5% to each of these returns. This new asset offers+4%, +7%, +9%, and +16%. Compute the expected rate of
What happens if you compute the average deviation from the mean, rather than the average squared deviation from the mean?
If a firm repurchases 1% of its shares, does this change the capitalization of the stock market on which it lists? If a firmpays 1% of its value in dividends, does this change the capitalization of
What are the three main types of investment companies as defined by the SEC?Which is the best deal in a perfect market?
What is the OTC market?
Insider trading is a criminal offense. Does the SEC prosecute these charges?
When and under what circumstance was the SEC founded?
What are the two main mechanisms by which a privately held company can go public?
Is NASDAQ a crossing market?
Roughly, how many firms are listed on the NYSE? How many are listed on NASDAQ?Then use a financial website to find an estimate of the current number.
Describe the differences between the NYSE and NASDAQ.
What extra function do retail brokers handle that prime brokers do not?
Explain the differences between a market order and a limit order.
Do individual stocks tend to move together?How could this be measured?
Looking at the figures in this chapter, did 20-year bonds move with or against the U.S. stock market? Did bonds move more or less with the U.S. stock market than the foreign stock, Sony?
Give an example in which a stock had a positive average rate of return, even though it lost its investors’ money.
Does the market beta of stocks in the market average out to zero?
How good are historical statistics as indicators of future statistics?Which kinds of statistics are better?Which kinds are worse?
Broadly speaking, what was the average risk of cash, bonds, and stocks? What time period are your numbers from?
Broadly speaking, what was the average rate of return on cash, bonds, and stocks? What time period are your numbers from?
Using the information in Table 7.1 on page 182, compute the discrepancy between arithmetic and geometric rates of return for cash and stocks.Which one is lower?Why?
Shares can disappear in a delisting or a repurchase.
Funds disappear from the public financial markets back into the pockets of investors through dividends and share repurchases.
The main mechanisms by which money flows from investors into firms are first IPOs and SEOs, and second reverse mergers, which are then sold off to investors.
In an open-end fund, you should purchase fund shares and request redemption. (You could short the underlying holdings during the time you wait for the redemption in order not to suffer price risk.)
The alternatives are often electronic, and they often rely on matching trades—thus, they may not execute trades that they cannot match. Electronic communication networks are the dominant example of
The specialist is often a monopolist who makes the market on the NYSE. The specialist buys and sells from his own inventory of a stock, thereby “making a market.” Market makers are the equivalent
A crossing system does not execute trades unless there is a counterparty. It also tries to cross orders a few times a day.
Your rate of return is higher if you short a stock in the perfect world because you earn interest on the proceeds. In the real world, your broker may help himself to this interest.
Prime brokers are usually used by larger investors. Prime brokers allow investors to employ their own traders to execute trades. (Like retail brokers, prime brokers provide portfolio accounting,
Brokers execute orders and keep track of investors’ portfolios. They also facilitate purchasing on margin.
The market beta of the market is 1—you are plotting the rate of return on the market on both the x-axis and the y-axis, so the beta is the slope of this 45◦ diagonal line.
To graph the market beta, the rate of return on the market (e.g., the S&P 500) should be on the x-axis, and the rate of return on the investment for which you want to determine the market beta should
Yes. For example, look at UAL in Table 7.1. It lost everything but still had a positive average arithmetic rate of return.
Usually (but not always), individual stocks are riskier.
The risk is usually increasing: lowest for cash, then bonds, then the stock market portfolio, and finally individual stocks. The average reward is increasing for the first three, but this is not
Note that because the returns in (b) and (c) alternate, you just need to work out the safe 2-year returns—thereafter, they will continue in their (unrealistic) patterns.(a) 5% for both.(b) Over 2
A compound return graph shows how a time series of rates of return interacts to produce long-run returns.In other words, you can see whether a long-run investment would have made or lost money. This
A histogram makes it easier to see how frequent different types of outcomes are—and thus, where the distribution is centered and how spread out it is.
A time-series graph shows how individual years matter. This can no longer be seen in a histogram.

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