FINA 469 Lecture Notes - Lecture 7: Covariance, Stock Fund
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Finance homework check! Risk loving, calculations, etc. I just need my answers checked!
Suppose Joe has the choice of two investments. He can invest in a bond, which in 10 years (not accounting for inflation), will have a 50% probability of a 50% return and a 50% probability of a 40% return. On the other hand, he could invest in a mutual fund that in 10 years would have a 50% chance of returning 100% and a 50% chance of returning -20%. If he chose the latter investment, would he be considered Risk Neutral, Risk Averse, or Risk Loving?
Joe would be considered as risk loving.
The later investment is high risk high return investment compared to the one before.
Now, Dr. Pennyworth has a chance to purchase one of two professional cricket clubs, the Miami Manatees or the Jacksonville Gemini. At the beginning of last year, the Manatees were purchased for $100 million, provided $10 million in profits, and are currently on sale for $110 million. On the other hand, the Gemini started the year purchased at $80 million, provided $30 million in profits, and are currently on sale for $140 million. Calculate the rate of return for the owners of each team last year. Which team would you suggest that Dr. Pennyworth purchase today?
Miami Manatees
Investment =$100 million
Return = $10 million
Rate of return = 10/100 = 10%
Selling price = $110 million
Jacksonville Gemini
Investment = $80 million
Return = $30 million
Rate of Return = 30/80 = 37.5%
Selling Price = $140 million
Dr. Pennyworth should purchase Jacksonville Gemini cricket club.
For the above problem, you project that the most optimistic profits for the Manatees this year is $35 million, while the most pessimistic projection is $5 million. Your projections for the Gemini are $32 million and $7 million, respectively. Based only on the range, which do you think is the riskier investment? Which one would you choose?
Game | Most optimistic | Most pessimistic |
Manatees | $35million | $5million |
Gemini | $32 million | $7million |
Based only on the range, Manatees is a riskier investment i.e. $30 million compared to $25million difference between the most optimistic and most pessimistic projection.
I would choose Manatees.
4. Imagine there are two free agent outfielders available. They both cost the same price, but you only have the money to sign one. Assume home runs alone are a proxy for performance. Suppose Player 1 has a 20% chance of hitting 20 home runs and a 20% chance of hitting 25 home runs, a 25% chance of hitting 30 home runs, a 20% chance of hitting 35 home runs, and a 15% chance of hitting 40 home runs. Player 2 has a 10% chance of hitting 10 home runs and a 10% chance of hitting 15 home runs, a 10% chance of hitting 25 home runs, a 30% chance of hitting 30 home runs, a 30% chance of hitting 35 home runs, and a 10% chance of hitting 50 home runs.
Which player has the highest expected return?
Player one expected return
0.2 *20 + 0.2*25 + 0.25*30 + 0.2*35 + 0.15*40 = 25.9 homes
Player two expected return
0.1*10+0.1*15+0.1*25+0.3*30+0.3*35+0.1*50= 24.5 homes
Which player would represent the riskier investment?
Player one | |||||
0.2 | 20 | 4 | -25.5 | 650.25 | 130.05 |
0.2 | 25 | 5 | -24.5 | 600.25 | 120.05 |
0.25 | 30 | 7.5 | -22 | 484 | 121 |
0.2 | 35 | 7 | -22.5 | 506.25 | 101.25 |
0.15 | 40 | 6 | -23.5 | 552.25 | 82.8375 |
Expected return | 29.5 | VARIANCE | 555.1875 | ||
STD DEV | 23.56 |
Player Two | |||||
0.1 | 10 | 1 | -23.5 | 552.25 | 55.225 |
0.1 | 15 | 1.5 | -23 | 529 | 52.9 |
0.1 | 25 | 2.5 | -22 | 484 | 48.4 |
0.3 | 30 | 9 | -15.5 | 240.25 | 72.075 |
0.3 | 35 | 10.5 | -14 | 196 | 58.8 |
0.1 | 50 | 5 | 5 | 25 | 2.5 |
Expected return | 24.5 | VARIANCE | 287.4 | ||
STD DEV | 16.95 |
Player 1 is a riskier investment i.e. Player 1 has higher variance and standard deviation
Which player would you choose?
I would choose player two
What does this say about your risk preferences?
I am risk loving
If there is a high chance of a negative return, why would a general manager invest in a very risky player? How might this conflict with the goals of the team as a whole?
A general manager would invest in a very risky player with a high chance of a negative return since probably the investment would generate huge profits if the estimation of the manager turns out to be correct is high.
The goals of the team as a whole are to maximize returns and minimize risk. Investing in a risky player raises the risk profile of the team as a whole.
Assume Mike Trout has the following distribution of outcomes for 2012. If he gets hurt, he will need some time to recover even while in the lineup, so he cannot produce at his highest level even if he comes back from an injury. If he does not get hurt, then he is certain to either Produce A, B or C, with A > B > C.
Outcome | Probability | Return/Production |
Gets Hurt, Misses Whole Season | 10% | 0 wins |
Gets Hurt, Misses 1/2 season, Produces B | 20% | 1.5 wins |
Gets Hurt, Misses 1/2 season, Produces C | 10% | 0.75 wins |
Gets Hurt, Misses 1/4 season, Produces B | 10% | 3 wins |
Gets Hurt, Misses 1/4 season, Produces C | 10% | 1.5 wins |
No Injury, Produces A | 20% | 10 wins |
No Injury, Produces B | 10% | 6 wins |
No Injury, Produces C | 10% | 3 wins |
Using the above information, calculate Mike Trout's expected production for next year. What is his range of possible performances?
Outcome | Probability | Return/Production | Expected Return | Ri - ER | Ri - ER)SQUARED |
Gets Hurt, Misses Whole Season | 10% | 0 | 0 | -3.725 | 13.87563 |
Gets Hurt, Misses 1/2 season, Produces B | 20% | 1.5 | 0.3 | -3.425 | 11.73063 |
Gets Hurt, Misses 1/2 season, Produces C | 10% | 0.75 | 0.075 | -3.65 | 13.3225 |
Gets Hurt, Misses 1/4 season, Produces B | 10% | 3 | 0.3 | -3.425 | 11.73063 |
Gets Hurt, Misses 1/4 season, Produces C | 10% | 1.5 | 0.15 | -3.575 | 12.78063 |
No Injury, Produces A | 20% | 10 | 2 | -1.725 | 2.975625 |
No Injury, Produces B | 10% | 6 | 0.6 | -3.125 | 9.765625 |
No Injury, Produces C | 10% | 3 | 0.3 | 3.425 | 11.73063 |
Total expected Return | 3.725 | ||||
Variance | 87.91188 | ||||
Standard deviation | 9.37 |
What about his standard deviation?
= 9.37
Using the standard deviation, calculate the interval within which Trout's performance should fall 95% of the time. Does anything seem strange about this calculation?
Standard error = 9.37/â (8) = 9.37/2.83 = 3.31
Margin of error = 3.31 x 2 = 6.61
95% confidence interval: 3.725 + 6.61 = -2.885 to 10.335
Something seems strange with this calculation. Margin of error is larger than the expected return
Suppose you could make an investment. With Investment 1, there is a 20% chance of making $10, a 15% chance of making $20, a 20% chance of making $25, a 20% chance of making $30, a 20% chance of making $40, and a 5% chance of making $100. For Investment 2, there is a 25% chance of making $1,000, a 50% chance of making $2,000, and a 25% chance of making $7,500. Use the coefficient of variation to evaluate the risk involved in these two investments. How does this result differ from using the range? How does it differ from comparing the two using only the standard deviation? Why is this important?
Investment 1 | Expected return | Variance | Square of Variance | |
0.2 | 10 | 2 | -27 | 729 |
0.15 | 20 | 3 | -26 | 676 |
0.2 | 25 | 5 | -1 | 1 |
0.2 | 30 | 6 | -23 | 529 |
0.2 | 40 | 8 | -21 | 441 |
0.05 | 100 | 5 | -24 | 576 |
Expected Return | 29 | |||
Variance | 2952 | |||
STD Dev | 54.33 | |||
Coefficient of variation = STD DEV/EXPECTED RETURN | 1.8734 |
Investment 2 | Expected return | Variance | Square of Variance | |
0.25 | 1000 | 250 | -2875 | 8265625 |
0.5 | 2000 | 1000 | -2125 | 4515625 |
0.25 | 7500 | 1875 | -1250 | 1562500 |
Expected Return | 3125 | |||
Variance | 14343750 | |||
STD Dev | 3787 | |||
Coefficient of variation = STD DEV/EXPECTED RETURN | 1.2118 |
Range
Investment 2âs returns are more skewed than investment 1 and therefore investment two would be considered riskier. However, using coefficient of variation shows that investment 1 is riskier.
Standard deviation
Investment has a higher standard deviation compared to investment 1 and therefore investment two would be considered riskier. However, using coefficient of variation shows that investment 1 is riskier.
Coefficient of variation measures the variability of the outcomes relative to the expected return. Since the two sets of data are different, coefficient of variation is the best measure of risk.
Based on the following table of yearly revenues, do you think the two teams are compliments or substitutes? Why?
Year | Manatees | Gemini |
2005 | $10 | $10 |
2006 | $5 | $15 |
2006 | $15 | $20 |
2008 | $25 | $35 |
2009 | $12 | $12 |
2010 | $12 | $15 |
2011 | $20 | $25 |
The teams are compliments. The price movements and range shows that Manatees and Gemini prices neither affect each other directly nor are they driven by the same set of factors as would be in the case of substitutes.
The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.
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2. The market value of any real or financial asset, including stocks, bonds, or art work purchased in hope of selling it at a profit, may be estimated by determining future cash flows and then discounting them back to the present.
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3. A bond has a $1,000 par value, makes annual interest payments of $100, has 5 years to maturity, cannot be called, and is not expected to default. The bond should sell at a premium if interest rates are below 10% and at a discount if interest rates are greater than 10%.
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4.Which of the following events would make it more likely that a company would choose to call its outstanding callable bonds?
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5. A 15-year bond has an annual coupon rate of 8%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 6%. Which of the following statements is CORRECT?
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6. Which of the following statements is CORRECT?
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7. Your investment account pays 6.8%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?
Select the correct answer.
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8. You want to purchase a motorcycle 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today?
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9. Suppose you earned a $135,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?
Select the correct answer.
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10.Your older brother turned 35 today, and he is planning to save $30,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at theend of his first retirement year.
Select the correct answer.
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11. Rogoff Co.'s 15-year bonds have an annual coupon rate of 9.5%. Each bond has face value of $1,000 and makes semiannual interest payments. If you require an 11% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
Select the correct answer.
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12. Haswell Enterprises' bonds have a 10-year maturity, a 6.25% semiannual coupon, and a par value of $1,000 . The going interest rate (rd) is 9.75%, based on semiannual compounding. What is the bond's price?
Select the correct answer.
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Question 5
The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.
True |
False |
Question 6.
In portfolio analysis, we often use ex post (historical) returns and standard deviations, despite the fact that we are interested in ex ante (future) data.
True |
False |
Question 7
Typically, debentures have higher interest rates than mortgage bonds primarily because the mortgage bonds are backed by assets while debentures are unsecured.
True |
False |
Question 8
If two firms have the same current dividend and the same expected growth rate, their stocks must sell at the same current price or else the market will not be in equilibrium.
True |
False |
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Question 9
Which of the following is the best measure of the wealth of a firm's stockholders?
The firm's Net Income during the past year |
Expected Earnings per Share during the coming year |
Book Value (or Net Worth) as recorded on the balance sheet |
The price of the firm's stock on the open market |
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Question 10
Consider the following firms:
Net Income | Stock Price at | Stock Price at | |
this year | Beg of Year | End of Year | |
Firm A: | $10,000,000 | $20 | $10 |
Firm B: | $(10,000,000) | $10 | $20 |
The manager of Firm A is doing a better job than B |
The manager of Firm B is doing a better job than A |
Neither manager is doing a good job |
Both managers are doing a good job |
Question 11
A company has the following income statement. What is its net operating profit after taxes (NOPAT)?
Sales $1,000
Costs 700
Depreciation 100
EBIT $ 200
Interest expense 50
EBT $ 150
Taxes (40%) 60
Net income $ 90
$ 90 |
$120 |
$150 |
$180 |
$200 |
Question 12
Carter Corporation has some money to invest, and its treasurer is choosing between City of Chicago municipal bonds and U.S. Treasury bonds. Both have the same maturity, and they are equally risky and liquid. If Treasury bonds yield 6 percent, and Carter's marginal income tax rate is 40 percent, what yield on the Chicago municipal bonds would make Carter's treasurer indifferent between the two?
2.40% |
3.60% |
4.50% |
5.25% |
6.00% |
Question 13
If a firm's current ratio is less than 1.0, it indicates that:
The firm had negative net income for the year |
The firm will be unable to pay its shortterm loans which come due this year |
Current Assets are less than Current Liabilities |
The firm is insolvent |
Question 14
A firm which has a relatively large amount of cash and receivables in its current assets accounts and a relatively small amount of current liabilities would be considered:
liquid |
profitable |
risky |
nuts |
Question 15
In November 2011 you bought 100 shares of Microsoft stock for $35.375 a share. In November 2013 you sold your stock for $92.5625 a share. What was your average annual rate of return on your Microsoft investment? (disregard dividends and commissions)
262% |
62% |
585% |
1.6% |
Question 16
You deposit $2,000 in a savings account that pays 10 percent interest, compounded annually. How much will your account be worth in 15 years?
$2,030.21 |
$5,000.00 |
$8,091.12 |
$8,354.50 |
$9,020.10 |
Question 17
You can earn 8 percent interest, compounded annually. How much must you deposit today to withdraw $10,000 in 6 years?
$5,402.69 |
$6,301.70 |
$6,756.76 |
$8,432.10 |
$9,259.26 |
Question 18
Calculate the required rate of return for Mercury, Inc., assuming that the real rate of interest is 3 percent, investors expect a 5 percent rate of inflation in the future, and they expect the rate of return on the overall stock market to be 13 percent. Mercury has a beta of 2.0.
15% |
16% |
17% |
18% |
None of the above |
Question 19
Which is the best measure of risk for an asset held in isolation? Which is the best measure for an asset held in a diversified portfolio?
Variance; correlation coefficient |
Standard deviation; correlation coefficient |
Beta; variance |
Coefficient of variation; beta |
Beta; beta |
Question 20
You have three stocks in your portfolio. $10,000 is invested in a stock with a beta of 1.50 and $15,000 is invested in a stock with a beta of 1.00, and $25,000 is invested in a stock with a beta of 0.50. What is the beta of your portfolio?
0.28 |
0.85 |
1.00 |
3.00 |
Question 21
A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?
$ 634.86 |
$1,064.18 |
$1,065.04 |
$1,078.23 |
$1,094.56 |
Question 22
The Jones Company has decided to undertake a large project. Consequently, there is a need for additional funds. The financial manager plans to issue preferred stock with a perpetual annual dividend of $5 per share and a par value of $30. If the required return on this stock is currently 20 percent, what should be the stock's market value?
$150 |
$100 |
$ 50 |
$ 25 |
$ 10 |
Question 23
A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 15 percent, and if investors require a 19 percent rate of return, what is the price of the stock?
$57.50 |
$62.25 |
$71.86 |
$64.00 |
$44.92 |
Question 24
A stock is not expected to pay a dividend over the next four years. Five years from now, the company anticipates that it will establish a dividend of $1.00 per share (i.e., D5 = $1.00). Once the dividend is established, the market expects that the dividend will grow at a constant rate of 5 percent per year forever. The risk-free rate is 5 percent, the company's beta is 1.2, and the market risk premium is 5 percent. The required rate of return on the companyâs stock is expected to remain constant. What is the current stock price?
$ 7.36 |
$ 8.62 |
$ 9.89 |
$10.98 |
$11.53 |