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FNCE 317 Chapter Notes - Chapter 2: Relative Risk, Risk Premium, Worst-Case Scenario Series

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burgundyfox167
15 Oct 2016
School
University of Calgary
Department
Finance
Course
FNCE 317
Professor
Tom Cottrell

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Document Summary

Exam #1 review answers: given the following probability distribution, calculate the expected return, variance and standard deviation for security j. Expected return = 0. 2*10% + 0. 6*15% + 0. 2*20% = 15% After much consideration, you"ve narrowed your investment choices to cannes yachts, Assume the firm names represent the core business. American movie theaters non-luxury good: the parker company"s stock has a beta of 1. 2. The risk-free rate is presently 5 percent and the market risk premium is 4%: calculate the required rate of return. 6% + 1. 2*4% = 10. 8: if investors interpret the increase in the risk-free rate to mean tighter money and therefore become pessimistic, the sml will shift. Calculate the new required return if the slope of the sml is now 0. 05. If other information is required to solve this, list what is needed. The return on the market is 11%: what are the expected return, variance, and standard deviation for a portfolio with an investment of.

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Related Questions

Hi guys could someone help me and explain in detail the two fundamental principles of investments – the risk/return tradeoff and diversification. Also, describe how asset allocation and the correlation of various securities within asset classes impact the riskiness of an investor’s portfolio.

I found an answer but it seems to me very long and not sure about it so can you help me out guys

ANS:

Risk /Return Tradeoff

Risk, return and liquidity are three dimensions of investment decision. Risk/Return trade off considers two dimension ie risk and return. As risk of an investment increases , its expected return will decrease. Risk is measured by volatility of return which can be statistically obtained by standard deviation of return. Higher the standard deviation, higher will be volatility of return and higher the risk

Risk can be also measured as a relative risk compared to the market. This is measured by stock beta with reference to a market index. Higher the beta, higher the value of stock Beta, higher will be the risk .

Investors seeking higher return will need to take higher risks.

Treasury bonds are almost risk free assets. This has the lowest rate of return. Stocks have higher risk , hence have higher expected return. High beta stocks will have higher risk and higher returns.

An investor should understand his risk taking ability and will have to make a trade off between risk and return depending on his risk apetite.

Diversification:

There is a saying, do not put all your eggs in one basket. The reason is that it has higher risk if all eggs are in one basket. If the eggs are distributed in different basket, risk of loss decreases.

Same principle is applied in investment. Diversification reduces risk.

If one invests in different classes of assets like bonds, stock, commodities and properties –his risk is likely to reduce. Reduction in return in one asset is likely to be compensated by return in other asset.

Within one class of asset also, there should be diversification to reduce risk.

For example one stock “A “may have expected return of 10% and standard deviation of 5%.This risk can be reduced by diversification in number of assets and the ratio of Risk/return can be decreased.

If we diversify and instead of investing 100% in stock A, we invest 60% in “A” and 40% in another stock “B” having expected return15% and standard deviation of 8%.assume the correlation between the two assets are 0.5

Portfolio return=wa*Ra+wb*Rb

Wa=Weight of asset A=0.6

Wb=Weight of asset B=0.4

Ra=Return of A=10%

Rb=Return of B=15%

Sa=Standard deviation of A=5%

Sb=Standard deviation of B=8%

Corr(a,b)=Correlation of A & B=0.2

Portfolio return=0.6*10+0.4*15=12%

Portfolio Variance=(wa^2)*(Sa^2)+(wb^2)*(Sb^2)+2wa*wb*Cov(a,b)

Cov(a,b)=Corr(a,b)*Sa*Sb=0.1*5*8=4

Portfolio Variance=(0.6^2)*(5^2)+(0.4^2)*(8^2)+2*0.6*0.8*4=23.08

Portfolio standard deviation=Square root of Variance=(23.08^0.5)=4.8%

The diversification has increased return and reduced risk

Stock A was giving 10% return with 5% standard deviation. With diversification of portfolio we have 12% return and 4.8% standard deviation. Risk return ratio is decreased.

It may be noted that, higher the correlation between assets in the portfolio, higher will be risk in terms of standard deviation. Hence it is better to diversify with uncorrelated assets.

Diversification reduces unsystematic risk,but it cannot reduce systematic risk of overall market or economy

Stocks X and Y have the following probability distributions of expected future returns:

Probability X Y
0.1 -15% -25%
0.2 6 0
0.3 10 24
0.3 20 27
0.1 33 40

Calculate the expected rate of return, rY, for Stock Y (rX = 12.00%.) Round your answer to two decimal places.
%

Calculate the standard deviation of expected returns, σX, for Stock X (σY = 18.21%.) Round your answer to two decimal places.
%

Now calculate the coefficient of variation for Stock Y. Round your answer to two decimal places.

Is it possible that most investors might regard Stock Y as being less risky than Stock X?

A. If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

B. If Stock Y is less highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be more risky in a portfolio sense.

C. If Stock Y is more highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be less risky in a portfolio sense.

D. If Stock Y is more highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

E. If Stock Y is more highly correlated with the market than X, then it might have the same beta as Stock X, and hence be just as risky in a portfolio sense.

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/√ (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 2’s 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.