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Important General Instructions:

For all the numerical problems in this assignment, do not round intermediate calculations.

Solve problems in the given units. IE: if given units are in $K, complete your computations in these units and, as applicable, report your answer in these units (without writing “$” or “K”).

Unless otherwise instructed, round your final answer to 3 decimal places, e.g., “32.162”. Note that if you type, for example, 41.350, Canvas will remove the last decimal place and record your answer as 41.35 This is fine because 41.35 = 41.350.

Report negative numbers like this: -23.451 Not like this: (23.451)

Do not report any numerical answer as a percent. IE: write 0.324 instead of 32.4%.

Assume interest rates and discount rates are compound annual rates unless otherwise specified.

Assume time is measured in years unless otherwise stated.

Consider this information for the next question:

Here is your boss’ unfinished analysis of some zero coupon bonds, as shown in the table. Your boss assumes CF1 of each bond is Bernoulli-distributed.

Q1:

In terms of of probability and statistics, which is the best way to characterize bond 1?

A. We expect bonds of this type to provide a CF1 of $100 about 50% of the time. However, we believe that, during other times this class of bonds will provide a CF1 of just $50. So, on average for this type of investment we expect a CF1 of about $75.

B. We believe that the bond’s price (CFo) and estimated return indicate that it is a High Yield bond.

C. We believe that the market price (CFo) of this bond (and others like it) is too high. We therefore recommend not purchasing this type of bond until market conditions become more favorable.

D. Our view is that, because the bond has a low expected-value return, it is a poor investment prospect.

E. Because past performance does not guarantee future results, it is imprudent to say anything about the potential performance of this bond.

F. We expect bonds of this type to provide a CF1 of $100 about 50% of the time. However, we believe that, during other times this class of bonds will provide a CF1 of just $75. So, on average for this type of investment we expect about a 13.6% return.

Consider this normal distribution graph and the information below for the next two questions:

You have analyzed 30 years of historical, annual returns of the SPY ETF. SPY aims to follow the performance of the S&P 500 Large Cap stock index. You found the average return = 15% and the standard deviation of returns = 25%. You plan to model future SPY returns (for better or worse) as normally distributed, based on your historical analysis.

Q2:

When returns are measured annually, which two statements are true regarding Value at Risk (VaR)?

A. The VaR return, or less, will be achieved about 10% of the time.

B. The VaR return, or less, will be achieved about 5% of the time.

C. Only one statement is true. In this case, this counts as the second correct answer.

D. On average, over the long haul, the VaR return or something worse will occur about once in 10 years.

E. On average, over the long haul, the VaR return or something worse will occur about once in 20 years.

Q3:

What is the probability that, in any given future year, the SPY return will be between -35% and + 40%?

This information is for all questions:

You are trying to make the least-risky portfolio possible from this set of ETFs. Risk is being measured by Standard Deviation of returns (sigma).

__ETF mu sigma__

A 10% 25%

B 8% 15%

Correlation Coefficient (rho), A to B: -50%

Q4:

If you emphasize the minimization of risk over high average returns, and you have to make your portfolio from either 100% of A or 100% of B, which would you choose?

A. Not enough information is provided to answer this question.

B. A

C. B

Q5:

What is the expected value return (mu) for a portfolio comprised of 50% A and 50%B?

Round your answer to three decimal places. Do not write your answer as a percent. IE: write 0.251 not 25.1%.

Q6:

What is the standard deviation (sigma) for a portfolio comprised of 50% A and 50%B?

Round your answer to three decimal places. Do not write your answer as a percent. IE: write 0.251 not 25.1%.

Q7:

Of the three possible portfolios discussed in this assignment, which is the least risky?

A. Portfolio comprised of 50% A and 50% B

B. Portfolio of only A

C. Portfolio of only B

D. Not enough information is provided to answer this question.

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