set 1_Investment.pdf

1. A young couple has made a nonrefundable deposit of the first months rent (equal to $1000) on a 6Emonth apartment lease. The next day they find a different apartment that they like just as well, but its monthly rent is only $900. They plan to be in the apartment only 6 months. Should they switch to the new apartment? What if they plan to stay 1 year? Assume an interest rate of 12% and the rent is paid at the beginning of each month?

2. Two copy machines are available. Both have useful lives of 5 years. One machine can be either leased or purchased outright; the other must be purchased. Hence there are a total of three options: A, B and C. The details are shown in the table (the first years maintenance payments, occurring at the beginning of each year, followed by revenues from resale.) the present values of the expenses of these three options using a 10% interest rate are also indicated in the table. According to a present value analysis, the machine of least cost as measured by the present value, should be selected; that is, option B

Problem set 1 Kensey Yoon, Spring 2016

Option A is a lease; Option B and C are purchase of two alternative machines. All have 5Eyear lives It is not possible to compute the IRR for any of these alternatives, because all cash flows are negative (except for the resale values). However, it is possible to calculate the IRR on an incremental basis. Find the IRR corresponding to a change from A to B. Is a change from A to B justified on the basis of IRR?

3. The stock section of this portfolio is made up of mostly Blamo stock. Blamo can behave in three

different ways over the next year depending on the state of the world:

	A	B	C
Initial outlay	6,000	30,000	35,000
Yearly expense	8,000	2,000	1,600
Resale value	0	10,000	12,000
Present value (@10%)	31,359	30,131	32,621

STATE	RETURN	PROBABILITY
GOOD	12%	30%
OKAY	4%	45%
BAD	E5%	25%

A) What is the expected return of the stock? B) What is the variance of the stock? C) What is the Sharpe ratio of the stock if the riskEfree rate is 5,4, or 2%?

D) If another company sells its own stock, Whamo stock, which is designed to always have a Sharpe Ratio of 0.3, which stock Blamo or Whamo is preferred for the different riskEfree rates and why?

1. A friend of yours tells you that in China two year zero coupon U.S. treasury bonds, 100 par sell for $95. What is the annualized riskEfree rate in this example? You happen to notice the same security can be purchased or sold domestically for $97, how do you arbitrage this position? How many times should you make this trade? How likely is it that your friends information is current and correct?
2. Dale the farmer and his brother Jake decide to sell the family farm. They will use the proceeds to invest in the stock market. As they can not agree on an investment choice, they split their money. Dale buys stock bull with his half million bull currently sells for $45 per share
3. A) What is Dales return if the stock price after one year is 35,43,or 53 dollars per share?
4. B) If Dale decides that he wants to earn money faster and his broker will allow him buy on the margin. His broker requires a 50% initial margin and he charges a 3% annual fee on the loan amount. If Dale invests all that he can, what is Dales return if the stock price after one year is 35,43, or 53 dollars per share?
5. C) Jake is certain his brother is always wrong so he decides to short bull. His broker requires a 50% initial equity position, which does not gain interest. What is Jakes return if the stock price after one year is 35,43, or 53 dollars per share?

6. You think that there will be a further slowdown in economic growth and you think that this will

hit the retail industry. You take a closer look at Target, one of the largest retailers in the US. On Google finance you see that over the yearEtoEdate return on Target stock is 14.5% while S&P has decreased by 14.8%. You call up your broker and ask her to short sell 200 shares of Target stock which is trading at 57. For collateral you put up 6,000 in cash. You decide to hold the short position for 1 year and you expect Target to pay a dividend of 0.60 over this period. In one year Target is trading at 45E sales and net income declined at Target. Assume that the brokerage account pays no interest.

A) When you open your position, what is the margin of your account? B) What is the return of your interest?

7. You are hired to make investment decisions for a large pension fund. You meet with representatives from the company to figure out what kind of choices to make. To get things started you try to figure out their risk preferences. You discuss the concept of risk and return

with them to figure out what their level of risk aversion is. You ask them if they would rather invest in portfolio that offers an expected rate of return of 10% and a standard deviation of 15% or in the short term money market which offers a riskEfree 5% rate of return. They say that they prefer the risky portfolio.

A) What is the maximum level of risk aversion for which the risky portfolio is still preferred to the risk free investment? What can you now say about the companys employees risk preferences? Hint: the easiest way to think about this is to find the level of risk aversion A for which an investor is indifferent between two investments

Now, you ask them: if a risky portfolio had an 18% standard deviation, at what rate of return would they prefer it to a riskEfree investment that offers 5%? They say the expected return would need to be at least 10%. They say that at that rate they would be exactly indifferent between the two investments

B) What can you determine about their risk preferences?

You decide to invest in the risky portfolio because your analysis suggests that the expected return is equal to 11%. Now news comes to the market that makes you revise your estimate of the portfolios standard deviation to 2E%. You can not reach representative by phone

C) Should you change the pension fund investments to a riskEfree investment which still offers 5%?

1. We are trying to get a sense of how an investor you are advising is trading off risk and return. After several long discussions you come to the conclusion that his level of risk aversion is somewhere between A=3 or 4. A) Draw the indifference curve in riskEreturn space corresponding to a utility level of 0.05 for an investor with a risk aversion coefficient A=3. Choose standard deviations ranging from 0 to 0.3 in 0.05 steps B) Now draw the indifference curve corresponding to a utility level of 0.05 for an investor with risk aversion coefficient A=4. C) Comparing your answers to part a and b. what do you conclude about the two indifference curves? Particularly, comment on the slope and how this reflects the differences in risk aversion.
2. You convince your client to think more about how to mix different assets. You first focus on splitting the investment between a broad based index of the US stock market (M) and TEbills. Your analysis tells you that E(rm)=9%, m=18% . TEbills offer a 2% riskEfree rate of return. A) You first take a close look at the investment choices. What is the Sharpe ratio of the market? B)If your investor wanted to achieve an expected return of 8% by mixing by TEbills and the market portfolio M, what fraction y of funds would she invest in the risky asset?

C) If your client has risk aversion A=3, what is her optimal investment weight y in the risky asset? What does your client have to do in order to achieve this optional mix of the two assets? D) Due to recent market turmoil following the failure of the US bailout, you update your estimate of future volatility over the next year to m=24%. What is the new optimal investment weight y?

10. After graduation you decide to start an actively managed fund, the S&P 500 plus. This fund

invests in all S&P 500 stocks, but does not use the same weights as the S&P 500 index. A) Before you begin your analysis, you start by collecting the necessary inputs. What inputs do you need for your analysis? What is the total number of inputs that you will need? B)How do you go about constructing the minimum variance frontier of the S&P 500 stocks? How do you find the optimal risky portfolio? C)you announce to your clients that you will not take any short positions in any of the stocks. What restrictions does this place on your investment weights?