Could anyone kindly answer the following question in detail :) Suppose that a st

Question

Could anyone kindly answer the following question in detail :)

Suppose that a stock price has an expected return of 13% p.a. and a volatility of 25% p.a. The stock price today is $50. Calculate the following: a. The expected price tomorrow. the standard deviation of the stock price tomorrow and b. 95% confidence interval for the price tomorrow. Assume 252 trading days per year. b. The expected stock price next year, the standard deviation of the price next year and a 95% confidence interval for the price year.

Explanation / Answer

Answer:

The expected price of the stock is given by:

E(ST) = S0 euT

Here

S0 is current market price of the stock = $50

u is expected return of the stock = 13%

and T is time period = 1/252 as there are 252 trading days

Now we can calculate the expected price tomorrow as:

E(S1/252) = $50 x e 0.13x(1/252)

              = $50.05

And standard deviation as:

Here   s = Volatility = 25% pa

Variance (ST) = S02 X e 2uT (es2T – 1)

Var (S1/252) = 502 x e2x0.13x(1/252) (e(0.25)2x 1/252 - 1)

                  = 0.623845

And standard deviation = square root of 0.623845 = 0.789 = 78.9%

Now we can calculate the expected price after a year as:

E(S1) = $50 x e 0.13x1

              = $56.97

And standard deviation as:

Here   s = Volatility = 25% pa

Variance (ST) = S02 X e 2uT (es2T – 1)

Var (S1/252) = 502 x e2x0.13x1 (e(0.25)2x 1- 1)

                  = 210.4734

And standard deviation = square root of 210.4734 = 14.507

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