FINA 2201 Chapter Notes - Chapter 8: Capital Asset Pricing Model, Risk Measure, Standard Deviation

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lilacmule890

14 Mar 2016

School

Northeastern University

Department

Finance & Insurance

Course

FINA 2201

Professor

Sidi Boubker Drissi Messouak

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Document Summary

The riskier the asset the higher the rate of return. An assets risk can be analyzed in two ways. On a stand-alone basis where the asset it considered by itself. On a portfolio basis, where the asset is held as one of a number of assets in a portfolio. No investment should be undertaken unless the expected rate of return is high enough to compensate for the perceived risk. Statistical measures of stand-alone risk (cid:1) (cid:1) (cid:1) (cid:1) The tighter the probability distribution the more likely the actual (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) outcome will be close to the expected value. Thus, the tighter the probability distribution the lower the risk. (cid:1) (cid:1) Standard deviation quantifies the tightness of the probability distribution: the small the standard deviation the tighter the distribution. Standard deviation is a measure of how far the actual return is likely to deviate from the expected return (cid:1) (cid:1) (cid:1) (cid:1) (cid:1)

Related Questions

Fill in the blank using a number of terms listed below (@1 point per question).

Beta coefficient, Bonds, CAPM, Cash flows, Change, CV, Convertible bonds, Correlation, Correlation coefficient, Debenture, Discount, Diversifiable risk, Expected return, Interest rate risk, Inverted, Junk Bonds, Market risk, More, Normal, Opposite, Probability distribution, Ratings, Reinvestment rate risk, Risk, Risk averse investor, Risk premium, Standard deviation

______________is the chance that some unfavorable event will occur. For instance, the risk of an asset is essentially the chance that the assetâs cash flows will be unfavorable or less than expected.

A __________________ is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome.

The ______________________is a statistical measure of the variability of a set of observations. The variance of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation.

The _______________________ is equal to the standard deviation divided by the expected return; it is a standardized risk measure which allows comparisons between investments having different expected returns and standard deviations.

A _______________________ dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their _______________________.

A ________________ is the difference between the rate of return on a risk-free asset and the expected return on Stock i which has higher risk.

_________________ is a model based upon the proposition that any stockâs required rate ofreturn is equal to the risk free rate of return plus a risk premium reflecting onl y the risk remaining after diversification.

_________________ is the tendency of two variables to move together. A _________________ of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions.

_________________ is that part of a securityâs total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. _________________ is also known as company specific risk. This risk can be eliminated by proper diversification.

The _________________ is a measure of a stockâs market risk, or the extent to which the returns on a given stock move with the stock market.

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.

viridianhippopotamus258

Please answer all of the following questions

1) The CAPM implies that:

a. investors may invest in assets with expected returns lower than the riskless interest rate.

b. no investor should invest in the risk-free asset.

c. the only relevant measure of risk is standard deviation.

d. the expected return on an efficient portfolio may be lower than the riskless interest rate.

2) In case of a simple CAPM being used to estimate a time series data:

a. the mean of a residual risk should be equal to zero.

b. the regression coefficient should be equal to zero.

c. the difference between the market return and the riskfree rate of return should be equal to zero.

d. the beta of the portfolio should be equal to zero.

3)Which of the following statements is true?

a. An increase in coupons increases the duration of the bond.

b. The longer the maturity of a bond, the greater will be its duration.

c. An increase in the interest rate decreases the duration of the bond.

d. Duration is a measure of the sensitivity of the equities.

4) Which of the following investment strategies is inconsistent with a "contrarian" philosophy

a. buying low, selling high

b. buying when odd-lot buying is lower than normal

c. buying when mutual fund cash positions are low

d. buying when most investment advisory services are bearish

e. selling after a market crash or decline

5) All other things equal, which of the following bond price is more sensitive to interest rate changes?

a. a 10 year bond with a 10% coupon

b. a 20 year bond with a 7% coupon

c. a 20 year bond with a 10% coupon

d. a 30 year bond with 7% coupon

6) Studies of firms classified on the basis of P/E ratios come to the conclusion that low-P/E-ratio stocks earn much higher returns, after adjusting for risk, than high-P/E-ratio stocks. This is because

a. low-P/E-ratio stocks are riskier than high-P/E-ratio stocks.

b. investors like low-P/E-ratio stocks.

c. low-P/E-ratio stocks are more likely to be undervalued.

7) Tests of market efficiency tend to

a. look for statistical dependencies that exist in price changes over time.

b. measure the nature of the impact of new information on security prices as that new information becomes available.

c. search for trading systems that might be able to generate supernormal profits.

d. all of the above

FINA 2201 Chapter Notes - Chapter 8: Capital Asset Pricing Model, Risk Measure, Standard Deviation

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