Question

Task 1: Compute the respective average, standard deviation, and covariance of monthly or daily stock returns. You can pick any two companies to download stock data for (daily or monthly

Covariance table will be in the form:

Var(stock1, stock1)	Cov(stock1, stock2)
Cov(stock1, stock2)	Var(stock2, stock2)

Note: Use STDEV.P in Excel for the standard deviation

Task 2: Using the obtained statistics fromQ1, calculate an equal weighted portfolio return and portfolio variance for the first portfolio using the below equations:

Equal weighted portfolio return:

E(R_P) = w₁(avg(r₁)) + w₂(avg(r₂));

where w is the weight of each stock in the portfolio. And avg(r₁) is the mean return for stock 1 and avg(r₂) is the mean return for stock 2.

Portfolio variance:

σ²_p = w₁²( σ²_s1) + w₂²( σ²_s2) + 2_*w₁ w_{2 *} σ_s1 σ_s2

Answer 1

Task 1) Following two stocks have been considered:

Stock 1: Apple Inc.

Stock 2: Pepsico

The monthly returns are calculated for the above two stocks for the period of the last twelve months as:

= (Price in current month - Price in old month)/Price in old month

Task 2) Equal weighted portfolio return, E(RP) = w1(avg(r1)) + w2(avg(r2)

For an equally weighted portfolio, w1 = w2 = 50% = 0.5

avg(r1) = mean return for stock 1 = 5.30%

avg(r2) = mean return for stock 2 = 0.77%

Equal weighted portfolio return, E(RP) = 0.5*5.30% + 0.5*0.77% = 3.03%

Portfolio variance: σ2p is calculated as:

w1 = weight of stock 1

w2 = weight of stock 2

w1 = w2 = 0.5 (Because equally weighted portfolio)

(σ1)^2 = Variance of Stock 1 = 0.61%

(σ2)^2 = Variance of Stock 2 = 0.27%

COV(1,2) = 0.26%

Hence, σ2p = (w1*σ1)^2 + (w2*σ2)^2 + 2*w1*w2*COV(1,2)

σ2p = (0.5^2)*0.61% +  (0.5^2)*0.27% +2*(0.5)^2*0.26% = 0.15% + 0.07% +0.13% = 0.35%

Hence, variance of equal weight portfolio = 0.35%