FIRE 311 Study Guide - Midterm Guide: Weighted Arithmetic Mean, Risk Aversion, Standard Deviation

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limebeaver717

19 Nov 2017

School

VCU

Department

Finance, Insurance and Real Estate

Course

FIRE 311

Professor

Kwon

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Document Summary

Chapter 8 - risk and return: definitions of probability and risk. Risk is the chance that an unexpected outcome will occur. Probability distribution is a listing of all possible outcomes with a probability assigned to each: expected returns given probabilities. Rate of return expected to be realized from an investment during its life. Which is the mean value of the probability distribution of possible returns. Is measured by computing weighted average of the outcomes using the probabilities as the weights: measures of risk: using standard deviation to measure stand alone risk sqrt(payoff-expected return)^(2) x probability). The smaller the value of sd, the tighter the probability distribution the lower the total risk associated with the investments: coefficient of variation: risk/return ratio. Calculated as the standard deviation by the expected return cv=risk/return. Useful where investments differ in risk and expected returns: risk aversion and required return. Risk-averse investors require higher rates of return to invest in higher-risk securities.

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.

QUESTION 18

Diversification refers to the _____.

	A.	reduction of the stand-alone risk of an individual investment,measured by the standard deviation of its returns, by combining itwith other investments in a portfolio
	B.	reduction of the systematic risk of an individual investment,measured by the standard deviation of its returns, by combining itwith other investments in a portfolio
	C.	reduction of the systematic risk of an individual investment,measured by its beta coefficient, by combining it with otherinvestments in a portfolio
	D.	reduction of the stand-alone risk of an individual investment,measured by its beta coefficient, by combining it with otherinvestments in a portfolio
	E.	reduction of the unsystematic risk of an individual investment,measured by its coefficient of variation, by combining it withother investments in a portfolio

QUESTION 19

Which of the following statements is true about capitalbudgeting analysis?

	A.	Higher discount rates are used for computing the net presentvalues (NPVs) of riskier cash flows.
	B.	The payback period method should be used for capital budgetingdecisions if the project has multiple cash outflows.
	C.	The payback period method should be used for capital budgetingdecisions if there is a conflict in the project rankings as per theNPV method and the IRR method.
	D.	The net present value (NPV) method should be used to evaluateindependent projects, and the internal rate of return (IRR) methodfor mutually exclusive projects.
	E.	A project with only cash outflows and no cash inflows would havetwo internal rates of return (IRRs).

5 points

QUESTION 20

Other things held constant, if the investors become less riskaverse, the new security market line (SML) would _____.

	A.	not be affected
	B.	shift down
	C.	shift up
	D.	have a steeper slope
	E.	have a less steep slope

blushplatypus515

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.

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FIRE 311 Study Guide - Midterm Guide: Weighted Arithmetic Mean, Risk Aversion, Standard Deviation

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