The following returns are predicted for XYZ, Inc. stock under three projected ec
ID: 1170470 • Letter: T
Question
The following returns are predicted for XYZ, Inc. stock under three projected economic scenarios.
Pi = Probability of economic scenario i. Ri = Return of ABC stock in economic scenario i.
Pi Ri
Boom 0.25 12
Normal 0.5 6
Recession 0.25 -2
What is the standard deviations of returns? If the returns are normally distributed, what is the expected range of returns assuming a 95% level of confidence. If the price of stock is currently $50, what is the expected range of prices using a 95% level of confidence.
Explanation / Answer
Expected return is calculable by formula:
Expected Return on Stock E(R) = 3% + 3% - 0.5% = 5.5%
Probability (Pi)
Return (Ri)
Pi * Ri
Sqrd Deviation
[E(R) – Ri]2
Sqrd Deviation * Pi
0.25
12%
3.00%
0.004225
0.00105625
0.5
6%
3.00%
0.000025
0.0000125
0.25
-2%
-0.50%
0.005625
0.00140625
(Standard Deviation)2 = (0.00105625 + 0.0000125 + 0.00140625) = 0.002475
Standard Deviation = 4.97%
Based on the statistics rule for normal distribution, for a normal distribution, 95% of confidence interval = Mean +/- 1.96(Standard Deviation)
Now, for our question, expected return is equivalent to mean.
Hence, 95% confidence interval range = [5.5% - (1.96 * 4.97%)] till [5.5% + (1.96 * 4.97%)] = -4.25% till 15.25%.
So, if stock price if $50, range of prices could be: $50* (1 – 4.25%) till $50 * (1 + 15.25%) = 47.875 till 57.625
Probability (Pi)
Return (Ri)
Pi * Ri
Sqrd Deviation
[E(R) – Ri]2
Sqrd Deviation * Pi
0.25
12%
3.00%
0.004225
0.00105625
0.5
6%
3.00%
0.000025
0.0000125
0.25
-2%
-0.50%
0.005625
0.00140625