Econ Midterm 1 (Chapter 5)
High oil prices tend to harm the auto industry and benefit oil companies; therefore, high oil prices are an example of: A. systematic risk. B. idiosyncratic risk. C. neither systematic nor idiosyncratic risk. D. both systematic and idiosyncratic risk.
B
Consider the following two investments. One is a risk-free investment with a $100 return. The other investment pays $2000 20% of the time and a $375 loss the rest of the time. Based on this information, answer the following: (i) Compute the expected returns and standard deviations on these two investments individually. (ii) Compute the value at risk for each investment. (iii) Which investment will risk-averse investors prefer, if either? Which investment will risk- neutral investors prefer, if either?
(i) The expected rate of return is $100 for the risk-free investment. The risk-free investment has a standard deviation of zero because the return is certain. For the risky investment: Expected return = 0.2($2000) + 0.8(-$375) = $100 Standard Deviation = 0.2 * (2000 - 100)2 + 0.8 * (-375 - 100)2 = 902500 = 950 (ii) The value at risk for the risk-free investment is $100 because it pays a certain return. The value of risk for the risky investment is -$375, this is the maximum amount the investor can lose. (iii) The risk-averse investor will prefer the risk-free investment. The risk-neutral investor will not have a preference between the two investments because they pay the same expected return.
A $500 investment has the following payoff frequency: half of the time it will pay $350 and the other half of the time it will pay $900. Its standard deviation and value at risk respectively are: A. $275; $150 B. $625; $275 C. $275; $350 D. $125; $500
A
An investment pays $1,200 a quarter of the time; $1,000 half of the time; and $800 a quarter of the time. Its expected value and variance respectively are: A. $1,000; 20,000 dollars2 B. $1,050; 20,000 dollars2 C. $1,000; 40,000 dollars2 D. $1,000; 80,000 dollar2
A
Another name for the expected value of an investment would be the: A. mean value. B. upper-end value. C. certain value. D. risk-free value.
A
Changes in general economic conditions usually produce: A. systematic risk. B. idiosyncratic risk. C. risk reduction. D. lower risk premiums.
A
Given a choice between two investments with the same expected payoff most people will: A. choose the one with the lower standard deviation. B. opt for the one with the higher standard deviation. C. be indifferent since the expected payoffs are the same. D. calculate the variance to assess the relative risks of the two choices.
A
Hedging is possible only when investments have: A. opposite payoff patterns. B. the same payoff patterns. C. payoffs that are independent of each other. D. the same risk premiums.
A
Sometimes spreading has an advantage over hedging to lower risk because: A. it can be difficult to find assets that move predictably in opposite directions. B. it is cheaper to spread than hedge. C. spreading increases expected returns, hedging does not. D. spreading does not affect expected returns.
A
The Russian wheat crop fails, driving up wheat prices in the U.S. This is an example of: A. idiosyncratic risk. B. diversification. C. systematic risk. D. quantifiable risk.
A
The variance of a portfolio of assets: A. decreases as the number of assets increases. B. increases as the number of assets increase. C. approaches 0 as the number of assets decreases. D. approaches 1 as the number of assets increases.
A
When measuring the risk of an asset: A. one must measure the uncertainty about the size of future payoffs. B. it is necessary to incorporate uncertainties that are not quantifiable. C. one must remember that the concept of risk applies only to financial markets, not to financial intermediaries. D. one cannot use other investments to evaluate the asset's risk.
A
When the home construction industry does poorly due to a recession, this is an example of: A. systematic risk. B. idiosyncratic risk. C. risk premium. D. unique risk.
A
Which of the following is true? A. Investments with higher risk generally have a higher expected return than risk-free investments. B. Investments that pay a return over a longer time horizon generally have less risk. C. Investments with a greater variance in the size of the future payoff generally pay a lower expected return. D. Risk-free investments are the best benchmark for measuring the risk of all investment strategies.
A
Which of the following statements is most correct? A. Usually higher expected returns are associated with higher risk premiums. B. Usually higher risk premiums are associated with lower expected returns. C. Usually lower expected returns are associated with higher risk premiums. D. Usually expected returns are not associated with risk premiums.
A
Which of the following statements is true? A. Leverage increases expected return and increases risk. B. Leverage increases expected return and reduces risk. C. Leverage decreases expected return but has no effect on risk. D. Leverage decreases expected return and increases risk.
A
You do some research and find for a driver of your age and gender the probability of having an accident that results in damage to your automobile exceeding $100 is 1/10 per year. Your auto insurance company will reduce your annual premium by $40 if you will increase your collision deductible from $100 to $250. Should you? Explain.
An increase of a deductible from $100 to $250 exposes you to an out-of-pocket possible loss of $150 when you have an accident. But the chances of incurring this out-of-pocket loss is 1/10(0.10) each year, so we can calculate the expected loss as E.L. = 0.1($150) + 0.9($0) = $15.00. Since this expected loss is less than the $40 in premium savings it makes good sense to increase the deductible.
13. If an investment has a 20%(0.20) probability of returning $1,000; a 30%(0.30) probability of returning $1,500; and a 50%(0.50) probability of returning $1,800; the expected value of the investment is: A. $1,433.33 B. $1,550.00 C. $2,800.00 D. $1,600.00
B
A $600 investment has the following payoff frequency: a quarter of the time it will be $0; three quarters of the time it will pay off $1000. Its standard deviation and value at risk respectively are: A. $750; $600 B. $433; $600 C. $0; $1000 D. $433; $1000
B
A risk-averse investor compared to a risk-neutral investor would: A. offer the same price for an investment as the risk-neutral investor. B. require a higher risk premium for the same investment as a risk-neutral investor. C. place more focus on expected return and less on return than the risk-neutral investor. D. place less focus on expected return than the risk-neutral investor.
B
Hedging risk and spreading risk are two ways to: A. increase expected returns from a portfolio. B. diversify a portfolio. C. lower transaction costs. D. match up perfectly positively correlated assets.
B
A risk-averse investor versus a risk-neutral investor: A. will never take a risk, while the risk neutral investor will. B. needs greater compensation for the same risk versus the risk neutral investor. C. will take the same risks as the risk neutral investor if the expected returns are equal. D. needs less compensation for the same risk versus the risk neutral investor.
B
A risk-averse investor will: A. never prefer an investment with a lower expected return. B. always prefer an investment with a certain return to one with the same expected return but that has any amount of uncertainty. C. always require a certain return. D. always focus exclusively on the expected return.
B
An investment will pay $2,000 half of the time and $1,400 half of the time. The standard deviation for this investment is: A. $90,000. B. $300. C. $1,700. D. $30.
B
An investment with a large spread between possible payoffs will generally have: A. a low expected return. B. a high standard deviation. C. a low value at risk. D. both a low expected return and a low value at risk.
B
Consider the following two assets with probability of return = Pi and return = Ri. Calculate the expected return for each and the standard deviation. Which one carries the greatest risk? Why?
Asset A Asset B P1 R1 P1 R1 .4 12% .2 11.5% .5 8.5% .5 10% .1 -2% .3 0% For asset A, the expected return = 0.4(12) + 0.5(8.5) + 0.1(-2.0) = 8.85% For asset B, the expected return = 0.2(11.5) + 0.5(10.0) + 0.3(0) = 7.30% For asset A, the standard deviation is 3.98 = SqR .4(12-8.85)^2 + .1(-2-8.85)^2 For asset B, the standard deviation is 4.81 = SqR .2(11-5-7.3)^2 +.5(10-7.3)^2 + .3(0-7.3)^2 Since asset B has a higher standard deviation than asset A, its return has higher risk.
An individual faces two alternatives for an investment: Asset A has the following probability return schedule: Prob of return Return (yield) % .25 11 .2 10.5 .2 9.5 .15 9 .1 6.5 .1 -1.0 Asset B has a certain return of 8.0%. If the individual selects asset A does she violate the principle of risk aversion? Explain.
Asset A provides an expected return of 8.65%. For the investor the 0.65% premium may be a large enough differential to compensate for the additional risk, so she may still be "risk averse".
If an investment offered an expected payoff of $100 with $0 variance, you would know that: A. half of the time the payoff is $100 and the other half it is $0. B. the payoff is always $100. C. half of the time the payoff is $200 and the other half it is $0. D. half of the time the payoff is $200 and the other half it is $50.
B
If the probability of an outcome equals one, the outcome: A. is more likely to occur than the others listed. B. is certain to occur. C. is certain not to occur. D. has unquantifiable risk.
B
In investment matters, generally young workers compared to older workers will: A. minimize expected return and focus more on variability. B. be less risk-averse. C. have equal concern for expected return and variability. D. be more risk-averse.
B
Risk-free investments have rates of return: A. equal to zero. B. with a standard deviation equal to zero. C. that are uncertain, but have a certain time horizon. D. that exhibit a large spread of potential payoffs.
B
Spreading risk involves: A. finding assets whose returns are perfectly negatively correlated. B. adding assets to a portfolio that move independently. C. investing in bonds and avoiding stocks during bad times. D. building a portfolio of assets whose returns move together.
B
The greater the standard deviation of an investment the: A. lower the return. B. greater the risk. C. lower the risk. D. lower the risk and return.
B
The main reason for diversification for an investor is to: A. take advantage of the fact that returns of assets are perfectly positively correlated. B. take advantage of the fact that returns on assets are not perfectly correlated. C. lower transaction costs. D. gain from the greater returns that come from greater risk.
B
The variance of a portfolio containing n assets with independent returns: A. increases as n increases. B. decreases as n increases. C. is constant for any n greater than two. D. does not change in a predictable way when n increases.
B
When considering different investments, a risk-averse investor is most likely to focus on purchasing: A. investments with the greatest spread in the expected rate of return. B. investments that offer the lowest standard deviation in the investments' expected rates of return for any given expected rate of return. C. only risk-free investments. D. investments with the lowest risk premium, regardless of the expected rate of return.
B
Which of the following statements is false? A. Diversification can reduce risk. B. Diversification can reduce risk but only by reducing the expected return. C. Diversification reduces idiosyncratic risk. D. Diversification allocates savings across more than one asset.
B
Which of the following statements is true? A. Leverage increases expected return while lowering risk. B. Leverage increases risk. C. Leverage lowers the expected return and lowers risk. D. Leverage lowers the expected return and increases risk.
B
Which of the following would not be included in a definition of risk? A. Risk is a measure of uncertainty. B. Risk can always be avoided at no cost. C. Risk has a time horizon. D. Risk usually involves some future payoff.
B
You buy an asset for $2500. The asset will return $3300 half of the time and $2700, the other half. The expected return is 20%(a gain of $500) and the standard deviation is 12%($300). How would using $1,250 of borrowed funds change the expected return and standard deviation specifically?
Borrowing 50% of the funds needed to purchase the asset is using leverage. It will double the expected return as well as the standard deviation. For example, if the asset returns the $3,300, the lender will have to be repaid $1,250, but this leaves $2,050 for you. If the asset returns $2,700 the lender still needs to be repaid, leaving $1,450 for you. Since each of these outcomes is equally likely, we can calculate the expected return and standard deviation of leverage. Expected value = ½($2,050) + ½($1,450) = $1,750. The $1,750 expected value on a $1,250 investment is an expected return of 40%. So the expected return doubled using leverage. The standard deviation can also be calculated: sd= SqR .5($2,050-$1,750)^2 + .5($1,450-$1,750)^2 = $300 or 24% of the actual amount invested. So while the expected return doubled, so did the standard deviation.
A portfolio of assets has lower risk than holding one asset, but the same expected return and higher transaction costs. Which of the following statements is most correct? A. The portfolio is attractive to people who are risk-averse and risk-neutral, but not to risk seekers. B. The portfolio is attractive to investors who are risk-neutral. C. The portfolio is not attractive to investors who are risk-neutral. D. The portfolio is attractive to investors who are risk seekers.
C
All other factors held constant, an investment: A. with more risk should offer a lower return and sell for a higher price. B. with less risk should sell for a lower price and offer a higher expected return. C. with more risk should sell for a lower price and offer a higher expected return. D. with less risk should sell for a lower price and offer a lower return.
C
An automobile insurance company on average charges a premium that: A. equals the expected loss from each driver. B. is less than the expected loss from each driver. C. is greater than the expected loss from each driver. D. equals 1/(expected loss) of each driver.
C
An automobile insurance company that writes millions of policies is practicing a form of: A. mutual fund. B. hedging risk. C. spreading risk. D. eliminating systematic risk.
C
An individual who is risk-averse: A. never takes risks. B. accepts risk but only when the expected return is very small. C. requires larger compensation when the risk increases. D. will accept a lower return as risk rises.
C
An investor practicing hedging would be most likely to: A. avoid the stock market and focus on bonds. B. purchase shares in general motors and buy U.S. treasury bonds. C. purchase shares in general motors and Amoco oil. D. put his/her invested funds in CDs.
C
An investor puts $1,000 into an investment that will return $1,250 one-half of the time and $900 the remainder of the time. The expected return for this investor is: A. $1,075 B. 5.0% C. 7.5% D. 15.0%
C
Comparing a lottery where a $1 ticket purchases a chance to win $1 million with another lottery in which a $5,000 ticket purchases a chance to win $5 billion, we notice many people would participate in the first but not the second, even though the odds of winning both lotteries are the same. We can perhaps best explain this outcome by: A. higher expected value for the lottery paying $1 million. B. higher expected value for the lottery paying $5 billion. C. lower value at risk for the lottery paying $1 million. D. higher value at risk for the lottery paying $1 million.
C
Diversification is the principle of: A. eliminating risk. B. reducing the risk we carry to just two. C. holding more than one asset to reduce risk. D. eliminating investments from our portfolio that have idiosyncratic risk.
C
If ABC Inc. and XYZ Inc. have returns that are perfectly positively correlated: A. adding XYZ Inc. to a portfolio that consists of only ABC Inc. will reduce risk. B. adding ABC Inc. to a portfolio that includes only XYZ Inc. will increase risk. C. adding XYZ Inc. to a portfolio that consists of only ABC Inc. will neither increase nor decrease the risk of the portfolio. D. adding XYZ Inc. to a portfolio that consists of only ABC Inc. will neither increase nor decrease idiosyncratic risk but will lower systematic risk.
C
If a fair coin is tossed, the probability of coming up with either a head or a tail is: A. ½ or 50 percent. B. Zero. C. 1 or 100 percent. D. Unquantifiable.
C
If an investment will return $1,500 half of the time and $700 half of the time, the expected value of the investment is: A. $1,250. B. $1,050. C. $1,100. D. $2,200.
C
If the returns of two assets are perfectly positively correlated, an investor who puts half of his/her savings into each will: A. reduce risk. B. have a higher expected return. C. not gain from diversification. D. reduce risk but lower the expected return.
C
In order to benefit from diversification, the returns on assets in a portfolio must: A. be perfectly positively correlated. B. be perfectly negatively correlated. C. positively correlated but not perfectly. D. have the same idiosyncratic risks.
C
Investment A pays $1,200 half of the time and $800 half of the time. Investment B pays $1,400 half of the time and $600 half of the time. Which of the following statements is correct? A. Investment A and B have the same expected value, but A has greater risk. B. Investment B has a higher expected value than A, but also greater risk. C. Investment A and B have the same expected value, but A has lower risk than B. D. Investment A has a greater expected value than B, but B has less risk.
C
Leverage: A. reduces risk. B. is synonymous with risk-free investment. C. increases expected rate of return. D. leads to smaller changes in the investment's price.
C
Systematic risk: A. is the risk eliminated through diversification. B. represents the risk affecting a specific company. C. cannot be eliminated through diversification. D. is another name for risk unique to an individual asset.
C
The difference between standard deviation and value at risk is: A. nothing, they are two names for the same thing. B. value at risk is a more common measure in financial circles than is standard deviation. C. standard deviation reflects the spread of possible outcomes where value at risk focuses on the value of the worst outcome. D. value at risk is expected value times the standard deviation.
C
The expected value of an investment: A. is what the owner will receive when the investment is sold. B. is the sum of the payoffs. C. is the probability-weighted sum of the possible outcomes. D. cannot be determined in advance.
C
The fact that not everyone places all of his/her savings in U.S. Treasury bonds indicates that: A. most investors are not risk averse. B. many investors are actually risk seekers. C. even risk-averse people will take risk if they are compensated for it. D. most people are risk-neutral.
C
The fact that over the long run the return on common stocks has been higher than that on long-term U.S. Treasury bonds is partially explained by the fact that: A. A lot more money is invested in common stocks than U.S. Treasury bonds. B. There are regulations on the interest rates U.S. Treasury bonds can offer. C. The risk premium is higher on common stocks. D. Risk-averse investors buy more common stock.
C
The risk premium for an investment: A. is negative for U.S. treasury securities. B. is a fixed amount added to the risk-free return, regardless of the level of risk. C. increases with risk. D. is zero (0) for risk-averse investors.
C
The standard deviation is generally more useful than the variance because: A. it is easier to calculate. B. variance is a measure of risk, where standard deviation is a measure of return. C. standard deviation is calculated in the same units as payoffs and variance isn't. D. it can measure unquantifiable risk.
C
Uncertainties that are not quantifiable: A. are what we define as risk. B. are factored into the price of an asset. C. cannot be priced. D. are benchmarks against which quantifiable risks can be assessed.
C
Unexpected inflation can benefit some people/firms and harm others. This is an example of: A. systematic risk. B. unmeasured risk. C. idiosyncratic risk. D. zero risk since the effects balance.
C
Up to what amount would a risk-neutral gambler pay to enter a game where on the flip of a fair coin, if you call the correct outcome the payoff is $2,000? A. More than $1000 but less than $2000. B. Up to $2,000. C. Up to $1,000. D. More than $1,500.
C
Which of the following investment strategies involves generating a higher expected rate of return through increasing risk? A. Diversifying B. Hedging risk C. Leverage D. Value at risk
C
he expected return from a portfolio made up equally of two assets that move perfectly opposite of each other would have a standard deviation equal to: A. 1.0 B. -1.0 C. 0.0 D. 0.5
C
A risk-averse investor will: A. always accept a greater risk with a greater expected return. B. only invest in assets providing certain returns. C. never accept lower risk if it means accepting a lower expected return. D. sometimes accept a lower expected return if it means less risk.
D
An investment pays $1,500 half of the time and $500 half of the time. Its expected value and variance respectively are: A. $1,000; 500,000 dollars B. $2,000; (250,000 dollars)2 C. $1,000; 250,000 dollars D. $1,000; 250,000 dollars2
D
An investment pays $1000 three quarters of the time, and $0 the remaining time. Its expected value and variance respectively are: A. $1,000: 62,500 dollars2 B. $750; 46,875 dollars C. $750; 62,500 dollars D. $750; 187,500 dollars2
D
An investment will pay $2000 a quarter of the time; $1,600 half of the time and $1,400 a quarter of the time. The standard deviation of this asset is: A. $600 B. $1,650 C. $47,500 D. $217.94
D
An investor puts $2,000 into an investment that will pay $2,500 one-fourth of the time; $2,000 one-half of the time, and $1,750 the rest of the time. What is the investor's expected return? A. 12.5% B. $250.00 C. 6.25% D. 3.125%
D
An investor who diversifies by purchasing a 50-50 mix of two stocks that are not perfectly positively correlated will find that the standard deviation of the portfolio is: A. the sum of the standard deviations of the two individual stocks. B. greater than the sum of the standard deviations of the individual stocks. C. greater than the standard deviation from holding the same balance in only one of these stocks. D. less than the standard deviation from holding the same balance in only one of these stocks.
D
Diversification can eliminate: A. all risk in a portfolio. B. risk only if the investor is risk averse. C. the systematic risk in a portfolio. D. the idiosyncratic risk in a portfolio.
D
If the probability of an outcome is zero, you know the outcome is: A. more likely to occur. B. certain to occur. C. less likely to occur. D. certain not to occur.
D
Inflation presents risk because: A. inflation is always present. B. inflation cannot be measured. C. there are different ways to measure it. D. there is no certainty regarding what inflation will be in the future.
D
Investing in a mutual fund made up of hundreds of stocks of different companies is an example of all of the following except: A. spreading risk. B. diversifying. C. risk reduction. D. increasing the variance of a portfolio.
D
Professional gamblers know that the odds are always in favor of the house (casinos). The fact that they gamble says they are: A. irrational. B. risk-neutral. C. risk-averse. D. risk seekers.
D
Suppose that Fly-By-Night Airlines Inc., has a return of 5% twenty percent of the time and 0% the rest of the time. The expected return from Fly-By-Night is: A. 10%. B. 0.1%. C. 0.2%. D. 1.0%.
D
The measure of risk that focuses on the worst possible outcome is called: A. expected rate of return. B. risk-free rate of return. C. standard deviation of return. D. value at risk.
D
Unique risk is another name for: A. market risk. B. systematic risk. C. the risk premium. D. idiosyncratic risk.
D
Which of the following individuals is least likely to use value at risk as an important factor in his/her investment decision? A. An individual considering a mortgage to buy his first home. B. A family considering purchasing health insurance. C. A policy maker considering regulation of depository institutions. D. A mutual fund manager choosing the allocation of investments in the fund's portfolio.
D
nvestment A pays $1,200 half of the time and $800 half of the time. Investment B pays $1,400 half of the time and $600 half of the time. Which of the following statements is correct? A. Investment A and B have the same expected value, but A has greater risk. B. Investment B has a higher expected value than A, but also greater risk. C. Investment A has a greater expected value than B, but B has less risk. D. None of the statements are correct.
D
Explain why a riskier asset offers a higher expected return.
Due to the higher risk, savers will require a risk premium be added to the risk free return in order to entice the asset.
Calculate the expected value, the expected return, the variance and the standard deviation of an asset that requires a $1000 investment, but will return $850 half of the time and $1,250 the other half of the time.
Expected value is = 0.5($850) + 0.5($1,250) = $1,050 Expected return = $1,050/$1,000 = 0.05 or 5.0% Variance = 0.5(850 - 1,050)2 + 0.5(1,250 - 1,050)2 = 40,000 dollars2 Standard deviation = the square root of the variance or in this case = $200
Explain why returns on assets compensate for systematic risk but not for idiosyncratic risk.
Idiosyncratic risk can be reduced through diversification. Systematic risk cannot since it affects all assets.
Identify at least three possible sources for a risk an individual may face in planning for retirement.
In planning for retirement an individual faces at least the following uncertainties: Life span, there is uncertainty regarding how long an individual's life will be. Unexpected inflation, no one knows what the inflation rate will be in the future. This makes earning a targeted real return difficult. Health problems or other unforeseen contingencies can use up funds that were being set aside for retirement.
Compute the expected return, standard deviation, and value at risk for each of the following investments: Investment (A): Pays $800 three-fourths of the time and a $1200 loss otherwise. Investment (B): Pays $1000 loss half of the time and a $1600 gain otherwise. State which investment will be preferred by each of the following investors, and explain why. (i) a risk-neutral investor. (ii) an investor who seeks to avoid the worst-case scenario. (iii) a risk-averse investor.
Investment (A) Expected return = 0.25(-$1200) + 0.75($800) = $300 Standard Deviation = sqrt[0.25 * (-1000 - 300)2 + 0.75 * (800 - 300)2 ] = 750000 = 866 Value at Risk = -$1200 Investment (B) Expected return = 0.5(-$1000) + 0.5($2000) = $500 Standard Deviation = sqrt[0.5 * (-1000 - 500)2 + 0.5 * (1600 - 500)2 ] = sqrt[1690000] = 1300 Value at Risk = -$1000 (i) The risk-neutral investor is indifferent between these two investments because they pay the same expected return. (ii) The investor who seeks to avoid the worst-case scenario will choose Investment (B) because it has the lower value at risk. (iii) The risk-averse investor will prefer Investment (A) because it has a lower standard deviation. This suggests that there is less uncertainty about the expected return relative to Investment (B).
What is the probability of tossing a pair of dice once and getting a 1? How about a 7?
It is impossible to toss two dice and get a 1, since the smallest number you can roll is a 2. So the probability of getting a 1 is 0. On the other hand a seven can be obtained a 6 different ways, and since there are 36 possible outcomes from a single roll of a pair of dice, the answer is 6/36 or 1/6 or 16.7%.
Explain the following: Risk results from the fact that more outcomes could happen than will happen.
Risk results from uncertainty, not knowing what will happen. For example before a coin is flipped we know that there are two possible outcomes, heads or tails. Once the coin is flipped, there will only be one outcome. The risk is in not knowing a priori what is going to happen. If there is only one possible outcome, there is certainty and therefore, no risk.
An individual faces two alternatives for an investment. Asset 'A' has the following probability of return schedule: Prob of return Return (yield) % .25 11 .2 10.5 .2 9.5 .15 9 .1 6.5 .1 -1.0 Asset 'B' has a certain return of 10.25%. If this individual selects asset 'A' does it imply she is risk averse? Explain.
Since both assets provide the same expected return, they would be equally attractive to an investor who is risk neutral. An investor who is risk averse would prefer Asset B, which provides the same expected return but with less risk than Asset A.
Briefly explain the difference between idiosyncratic risk and systematic risk. Provide an example of each.
Systematic risk is risk resulting from something that will impact all firms, such as a general slowdown in the economy. Idiosyncratic risk will impact specific firms or industries, such as a harmful bacterium that is discovered in beef.
Calculate the expected value of an investment that has the following payoff frequency: a quarter of the time it will pay $2,000, half of the time it will pay $1,000 and the remaining time it will pay $0.
The expected value = ¼($2000) + ½($1000) + ¼($0) = $1000
What is the expected value of a $100 bet on a flip of a fair coin, where heads pays double and tails pays zero?
The expected value of this event is calculated as E.V. = PH (H) + PT(T); where H is the payoff from the coin turning up heads and T is the payoff if the coin turns up tails. PH and PT are the probabilities of the coin turning up heads or tails respectively. Substituting actual values in out formula reveals: E.V. = 0.5($200) + 0.5($0) = $100
What would be the standard deviation for a $1000 risk-free asset that returns $1,100?
The standard deviation for this asset would have to be $0. If it is truly risk-free the return is certain, and if the return is certain there is no variance in the return, therefore no standard deviation.
Why isn't it correct to say that people who are risk averse avoid risk?
This statement really isn't correct. A better statement would be that people who are risk averse need to be compensated to take additional risk. The degree of additional compensation is referred to as the risk premium and this will vary depending on the degree of risk aversion.
If there are 1,000 people, each of whom owns a $100,000 house, and they each stand a 1/1,000 chance each year of suffering a fire that will totally destroy their house, what is the minimum that they would have to pay annually for fire insurance?
We can calculate the expected loss for any one individual as: E.L. = 0.001($100,000) + 0.999($0) = $100.00. Since the expected loss for each individual is $100 per year, the minimum that each would have to pay is $100.00 a year, in fact, given the probability of 1 in a 1000 homeowners in this group suffering a fire each year, at $100 each, on average, there should be just enough to compensate the person suffering the fire.
What would be the impact of leverage on the expected return and standard deviation of purchasing an asset with 10% of the owner's funds and 90% borrowed funds?
We can use the general formula: Leverage factor = Cost of Investment/Owner's Contribution to the Purchase In this case the leverage factor would be 10; so the expected return and the standard deviation would both increase by a factor of 10.
An individual owns a $100,000 home. She determines that her chances of suffering a fire in any given year to be 1/1000(0.001). She correctly calculates her expected loss in any year to be $100. Explain why this really isn't a good way to measure her potential for loss.
While all of her calculations may be accurate this individual may be better off considering value at risk, which is the worst outcome. The value at risk from a fire for her in this case is $100,000 which, if suffered, could prove devastating.