Topic 1: Financial Markets
1. You are among the OTC market makers in the stock of Bio-Engineering, Inc. and quote a bid of 102 1/4 and an ask of 102 1/2. Suppose that you have a zero inventory.
(a) On Day 1 you receive market buy orders for 10,000 shares and market sell orders for 4,000 shares. How much do you earn on the 4,000 shares that you bought and sold? What is the value of your inventory at the end of the day? (Hints: It is possible to have negative inventory. Further, there is more than one correct way to value an inventory, but please state what assumption your valuation is based on.)
I buy 4000 shares at the price of 102 ¼, for which the total cost is $409,000. I sell the ...view middle of the document...
(c) What is a market maker's objective? Is there anything you could have done during Day 1, consistent with a market maker's objective that would have improved your performance over the two-day period?
The market-maker’s objective is to make money on the bid-ask spread, by buying stock at a lower price than the price at which they sell it, or selling the stock at a higher price than they buy it back. To improve performance over the two day period, I could have avoided completing a full buy order on the 1st day to avoid the short balance.
Topic 2: Performance Measures
2. Suppose a 5-year zero-coupon Treasury bond with face value $1000 has a 5% yield (annually compounded).
(a) What price does this bond sell for?
FV = $1000
t = 5 years
r = 5%
PV= FV / (1 + r)^t = $1000 / (1.05)^5 = $783.53
(b) Suppose another zero-coupon Treasury bond also has a 5% yield, but sells for $325:57. What is the maturity of this bond?
FV = PV (1 + r)^t
$1000 = $325.57 (1.05)^t
Solve for (t) -> t = 23 year maturity
3. Which of the following investments do you prefer?
(a) Purchase a zero-coupon bond, which pays $1000 in ten years, for a price of $550.
$1000 = $ 550 (1 + r )^10
R = 6.166% is the implied interest rate
(b) Invest $550 for ten years in Chase at a guaranteed annual interest rate of 5.5%.
FV = $ 550 * (1.055) ^ 10 = $939.47%
In both options, the value we pay today is $550. We calculated the implied interest rate which was 6.166% on part a). The first investment is a better deal because it provides the higher return for 10 years.
4. Suppose you get for free one of following two securities: (a) an annuity that pays $10,000 at the end of each of the next 6 years; or (b) a perpetuity that pays $10,000 forever, but payments do not begin until 10 years from now (the first cash payment from this security is 11 years from today).
Which security would you choose if the annual interest rate is 5%?
Does your answer change if the interest rate is 10%? Explain why or why not.
a) Annuity : (pays a fixed cash flow C, for T periods)
PV = C/R * (1 – 1/(1+R)^t)
PV = C * PV Factor = $10,000 * 5.07 = $50,700
PV Factor = [1 – 1/(1+R)^t ] / R = [1 – 1/(1.05)^6 ] / 0.05 = 5.07
b) Perpetuity: PV = (C/R) – pays a fixed cash flow every period forever. The value of perpetuity which begins in 11 years:
PV = C/R ( 1/ (1+R)^t) = $10000/ 0.05 * (1/1.05^10) = $122,784.78
Perpetuity is a better deal
SOLVING for 10% interest rate
Annuity => PV = PV = C/R * (1 – 1/(1+R)^t) = $ 43,552.61
Perpetuity => PV = C/R ( 1/ (1+R)^t) = 10000/ 0.1 * (1/1.1^10) = 38,544.32
Annuity is a better deal when interest rate is 10%.
5. Suppose a hedge fund manager earns 1% per trading day. There are 250 trading days per year. Answer the following questions:
(a) What will be your annual rate of return on $100 invested in her fund if she allows you to reinvest in her fund the 1% you earn each day?