Question

Q9. You are doing research on a biotech firm. You think there are three scenarios for the drug depending on the results from the clinical trials:

i. Not effective; ii. Effective; iii. Super effective

with probabilities of i 30%; ii. 40%; iii. 30%

respectively.

You believe the stock with be worth i. $50; ii. $100; iii. $150

under those scenarios eventually.

Q9a. What is the STDEV today? (3 points)

Q9b. A preliminary trial was NOT very promising, which eliminates the chance of iii (ie “supereffective”). What is the stock price reaction (what is the new price) upon the release of the trial result? (3points)

Q9c. What is the price of a PUT option with strike of 100 BEFORE and AFTER the news release? (4points)

Answer 1

Answer 1: To calculate the standard deviation, we need to follow these steps:

(a) first need to calculate the expected value (mean), as follows:

Expected (Mean) Value of Stock = (Probability of Scenario 1 x Value of Stock in Scenario 1) + (Probability of Scenario 2 x Value of Stock in Scenario 2) + (Probability of Scenario 3 x Value of Stock in Scenario 3)

= (30% x 50) + (40% x 100) + (30% x 150)

= 15 + 40 + 45

= USD 100

(b) We calculate the variance, as follows

Variance = (Probability for scenario 1 x (value of stock in scenario 1 – expected value of stock)2) + (Probability for scenario 2 x (value of stock in scenario 2 – expected value of stock)2) + (Probability for scenario 3 x (value of stock in scenario 3 – expected value of stock) 2)

= (30% x (50-100)2) + (40% x (100-100)2) + (30% x (150-100)2)
= (30% x (-50) 2) + (40% x (0) 2) + (30% x (50) 2)
= (30% x 2500) + (40% x 0) + (30% x 2500)
= 750 + 0 + 750
=USD 1,500

(c) We will finally calculate Standard deviation, as follows:
Standard Deviation = (Variance)sq. root
= (1500)sq. root
= USD 39

Answer 2: In this question, we are given 3 scenarios with 30%, 40% and 30% probabilities (i.e. sum total of 100% probability), respectively. Scenario 3 is eliminated, which means its probability becomes 0%. Now we need to distribute the 100% between 2 scenarios. Since, Scenario 1 and 2 were originally in the ratio 3:4, we will distribute 100% of the total probability in the same ratio.

The new probabilities would be as follows:

Probability of Scenario 1 = 100% x 3/(3+4)
= 100% x (3/7) = 42.86%

Probability of Scenario 2 = 100% x 4/(3+4)
= 100% x (4/7) = 57.14%

Therefore, new expected value (formula in the previous section) = (42.86% x 50) + (57.14% x 100)
= 21 + 57 = USD 78

Answer 3: Put Option is a contract (not mandatory, i.e. to the owners will to exercise), which gives the owner a right to sell an underlying asset at a predetermined price (also called strike price).

Intrinsic value of a Put option = Strike Price – Value of the underlying asset

Before the News, we had following values:

Value of the Stock = USD 100 (calculated in the first step of part 1)

Strike Price (given here) = USD 100

Therefore Intrinsic Value = 100 – 100 = USD 0

After the News, we had following values:

Value of the Stock = USD 78 (calculated in the part 2)

Strike Price (as given) = USD 100

Therefore Intrinsic Value = 100 – 78= USD 22