| Exercise 3 (20 points): You are considering several strategies involving the common stock and options of Goldman Sachs (GS). You have determined that there are three possible states of GS stock price 6 months from now: (1) Decline of 25%, (2) Unchanged, (3) Increase of
| 35% |
. Use this information to answer the following questions. (You should assume that the risk-free rate is zero. That is, any premiums received will have the same time value 6 months from now. You should also assume that no dividends are paid over the holding period. For consistency purposes, calculate HPRs with only the current stock price as the denominator and combined stock and options net profit or loss in the numerator)
(a)
| First, consider a covered call strategy involving the purchase of GS stock and a
|
| $230 |
strike price call. What is the 6 month holding period return (before any taxes) from this covered call strategy in all three return states?
| Call
| Strike Price |
$230
|
| Call Premium |
| $2.75 |
| Covered Call HPR with GS Decline |
| Covered Call HPR GS Unchanged |
| Covered Call HPR with GS Increase |
| Current GS Stock Price |
| $210 |
| (1) Decline in Down State |
-25% |
(b)
Next, consider a protected put strategy involving the purchase of GS stock and a
|
| $190 |
strike price put. What is the 6 month holding period return (before any taxes) from this protected put strategy in all three return states?
| (2) Unchanged Return |
0%
| (3) Increase in Up State |
35%
Option Time to
Expiration (Years) |
0.5
|
| Put Strike Price |
$190
|
| Put Premium |
| $3.00 |
| 6 Month Options Chain for Goldman Sachs (GS) |
Protected Put HPR with GS Decline |
| Call Price |
Strike Price
Put Price |
Protected Put HPR GS Unchanged |
|
| $40.00 |
$170 |
$0.90 |
Protected Put HPR with GS Increase |
| $32.50 |
$180 |
$1.75 |
| $24.00 |
$190 $3.00 (c)
Finally, consider a collar strategy involving the purchase of GS stock, a call at a
|
| $220 |
strike price, and a put with a
| $200 |
strike price. What is the 6 month holding period return (before any taxes) from this collared equity strategy in all three return states?
|
| $15.00 |
$200
| $4.75 |
| $9.00 |
$210
$10.00 |
|
| $5.25 |
$220 $15.00
$2.75 $230
| $21.50 |
Call Strike Price |
$220
| $1.25 |
$240 |
$33.00 |
Call Premium $5.25
| $0.75 |
$250 |
$40.00 Put Strike Price $200
Put Premium $4.75
| Collared Equity HPR with GS Decline |
| Collared Equity HPR GS Unchanged |
| Collared Equity HPR with GS Increase |
| (d) |
Calculate the standard deviation of returns across each state of GS returns (assuming each state is equally likely to occur) for each strategy. If your boss tells you he/she needs you to minimize risk across all states, which of these three strategies (Covered Call, Protected Put, or Collared Equity) are you going to choose? |
| Standard Deviation of Covered Call |
| Standard Deviation of Protected Put |
| Standard Deviation of Collared Equity |
| Risk Minimizing Strategy |
