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c. A portfolio consists of three securities P, Q and R with the following parameters: P Q R 25 22 20 24 Expected return (%) Standard deviation (%) Correlation: PQ QR PR 30 26 Correlation - 0.50 +0.40 + 0.60 If the securities are equally weighted, how much is the risk and return of the portfolio of these three securities? ​

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Answer:

To calculate the risk and return of the portfolio, we first need to calculate the portfolio's expected return and standard deviation.

Since the securities are equally weighted, each security has a weight of 1/3 in the portfolio.

Expected return of the portfolio:

Expected return = (weight of P x expected return of P) + (weight of Q x expected return of Q) + (weight of R x expected return of R)

Expected return = (1/3 x 25) + (1/3 x 22) + (1/3 x 20)

Expected return = 22.33%

Standard deviation of the portfolio:

We can use the formula for portfolio standard deviation:

σp = √[w1^2σ1^2 + w2^2σ2^2 + w3^2σ3^2 + 2w1w2ρ12σ1σ2 + 2w1w3ρ13σ1σ3 + 2w2w3ρ23σ2σ3]

where:

w1, w2, w3 are the weights of the three securities in the portfolio (1/3 each in this case)

σ1, σ2, σ3 are the standard deviations of the securities

ρ12, ρ13, ρ23 are the correlations between the securities

Substituting the given values, we get:

σp = √[(1/3)^2(25)^2 + (1/3)^2(22)^2 + (1/3)^2(20)^2 + 2(1/3)(1/3)(0.30)(25)(22) + 2(1/3)(1/3)(0.60)(25)(20) + 2(1/3)(1/3)(0.40)(22)(20)]

σp = 2.78%

Therefore, the risk and return of the portfolio are 22.33% and 2.78%, respectively.

Step-by-step explanation:

User Mmdts
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