Foundations of Financial Markets

In: Business and Management

Submitted By golpillar
Words 647
Pages 3
David Y. Kim
Section 004, Foundations of Financial Markets
Professor Jeffrey Wurgler
Homework 1

1. Bid = 102 ¼, Ask = 102 ½ a. Buy = 4,000(102.25) = $409,000
Sell = 4,000(102.50) = $410,000
Profit = $410,000 – $409,000 = $1,000
Value of Inventory at Ask price = –6,000(102.50) = –$615,000 b. New Bid = 110.25, New Ask = 110.5
Sell = 2,000(110.5) = $221,000
Buy = 8,000(110.25) = $882,000
Sold 6,000 shares yesterday for 6,000(102.50) = $615,000
Loss = $221,000 – $882,000 + $615,000 = –$46,000
Inventory = –2,000 + 8,000 – 6,000 = 0 c. A market maker’s objective is to profit off the bid-ask spread, mostly by creating a market and undercutting the market price. To improve performance, you could have avoided filling the entire buy order. If you sold only a portion of the buy order on the first day, you wouldn’t have to be short 6,000 shares overnight before the price jump.

2. d. Price bond is selling for = 1,000/(1+0.05)^5 = $783.53 e. Maturity:
325.57 = 1,000/(1+0.05)^t
(1+0.05)^t = 3.072 t = log(3.072)/log(1.05) = 23 years

3. Future Value of Option A = $1,000
Future Value of Option B = 550(1+0.055)^10 = $939.40

Because the FV of Option A is larger than the FV of Option B ($1,000 < $939.40), Investment A is preferable.

4. Annual interest rate of 5%
Annuity
PV = (C/r)(1 – 1/(1+r)^t)
PV = (10,000/0.05)(1 – 1/(1+0.05)^6)
PV = $50,756.92

Perpetuity
PV = (C/r)(1/(1+r)^t)
PV = (10,000/0.05)(1/(1+0.05)^10)
PV = $122,782.65

The perpetuity that begins in 10 years is preferable, since the present value of the perpetuity exceeds the present value of the annuity.

Annual Interest Rate of 10%
Annuity
PV = (C/r)(1 – 1/(1+r)^t)
PV = (10,000/0.1)(1 – 1/(1+0.1)^6)
PV = $43,552.61

Perpetuity
PV = (C/r)(1/(1+r)^t)
PV = (10,000/0.1)(1/(1+0.1)^10)
PV = $38,554.33

The annuity is…...

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