Question

An investor purchased 550 shares of stock A at $22.50 per share and 1,050 shares of stock B at $30.50 per share one year ago. Stock A and stock B paid quarterly dividends of $2.50 per share and $2.00 per share, respectively, during the year. One year later, the investor sold both stocks at $30.50 per share. The correlation coefficient (ρ_AB) is 0.3 and the standard deviations of stock A and stock B are 20.5 percent and 15.5 percent, respectively.

Calculate the standard deviation of the portfolio. (Round intermediate calculations to 4 decimal places, e.g. 15.2512 and the final answer to 2 decimal places, e.g. 15.25%.)

Answer 1

In the first step we will find the weights of each stock A & B in the portfolio

Stock	No. of Units (a)	Purchase Price per share (b)	Total Purchase Value (c = a xb)	% Weight in Portfolio d = c/Total Porfolio Val
A	550.00	22.50	12,375.00	= 12375/ 44400 = 27.8716%
B	1,050.00	30.50	32,025.00	= 32050/44400 = 72.1284%
Total			44,400.00	100.00%

Wa = 27.87%

Wb = 72.13%

Returns on stock = (Sales Price + Dividend Earned - Purchase Price) / Purchase Price

Annual Dividend on A = Quarterly Dividend x 4 = $2.5 x 4 = $10

Returns on stock A = 30.50 (Sales Price) + 10 (Dividend) - 22.50 (Purchase Price) / 22.50 (Purchase Price) = 18/22.50 = 80%

Similarly Returns on stock B = 30.50 (Sales Price) + 8 (Dividend) - 30.50 (Purchase Price) / 30.50 (Purchase Price) = 8/30.50 = 26.23%

Coefficient of Correlation of A&B = 0.30

SDA = Standard Deviation of Stock A = 20.5%

SDB = Standard Deviation of Stock B = 15.5%

The formula for portfolio Standard Deviation of stocks

= { WA2 SDA2 + WB2 SDB2  + 2 WA X SDA X WB X SDB X Coefficient of Correlation between A & B}^(1/2)

Where

WA = Weight of Stock in portfolio

SDA = Standard Deviation of Stock A

WB = Weight of Stock B in portfolio

SDB = Standard Deviation of Stock B

Computing Values SD of Portfolio A & B =

= (0.0776 x 0.0420 + 0.5202 x 0.0240 + 2 X 0.3 X 0.2787 x 0.7212 X 0.205 X 0.1550) ^ (1/2)

(0.01959)^(1/2) = 13.99%

We have calculated returns, although it wasnt required to calculate portfolio Standard Deviation