P1.T4.Ch1.Q13

[Harshita Phalor]

GARP- Book 2- Valuation- Chapter 1- Question 13

1. For the two investments considered in Table 1.2 and Figure 1.2, what are the risk-return combinations if the correlation is 0.15 instead of 0.25?

Can somebody help me understand how to solve this, thanks.

 

[David Harper CFA FRM]

Hi @Harshita Phalor GARP's solution is correct. See below. You need to apply the formula for a two-asset portfolio variance; e.g., given ρ = 0.15, when the weight is 0.40 in Asset 1, then:

• Portfolio variance, σ^2 = w1^2*σ1^2 + w2^2*σ2^2 + 2*w1*w2*σ1*σ2*ρ, in this case:
• σ^2 = 0.40^2*0.12^2 + 0.60^2*0.16^2 + 2*0.40*0.60*0.12*0.16*0.15 = 0.0129024; and portfolio volatility, σ = SQRT(0.0129024) = 0.113589, or about 11.4% per the rounded valued shown on the fourth row (final column).

Here is an xls https://www.dropbox.com/s/sfaifs1p383xi5j/011321-2assetportfolio.xlsx?dl=0