Question

The most recent weekly closing prices for a stock are provided below. The stock also pays dividends at a continuous rate of 2^%.

Week	Price
1	84
2	88
3	83
4	86
5	86

Calculate the annualized historical volatility of the stock. ?

Calculate the expected rate of appreciation of the stock. ?

(NO EXCEL WORK. PLEASE SHOW STEP BY STEP WITH FORMULA.)

Answer 1

a) The first part is just finding the standard deviation.

Average Stock Price :( 84+88+83+86+86)/5=85.40

Week	Price	(Price -Average Price)^2
1	84	1.96
2	88	6.76
3	83	5.76
4	86	0.36
5	86	0.36
	Sum	15.2

Therefore standard deviation= sqrt(15.2/5-1)= sqrt(15.2/4)=sqrt(3.8)=1.949%

This is weekly standard deviation. The question asks for annualized. There are 52 weeks in a year, and remember that volatility always scales by the square root of time.

1.949*sqrt(52)= 14.05702671%

b) We can use the implied growth rate formula to calculate stock price appreciation or growth rate (g)

D/P = r-g/(1+g)

D/P dividend Yield= 2%

g= growth rate (unknown)

r= discount rate (this is missing information)

=0.02= r- g/(1+g)

=g/(1+g)=r-0.02

Just plug in the value of r and solve for g