Assume the standard deviation of the U.S. market portfolio is 18.2%, the standard deviation of the non-U.S. portion of the world portfolio is 17.1%, and the correlation between the U.S. and non-U.S. market portfolios is .47. Suppose you invest 25% of your money in the U.S. stock market and the other 75% in the non-U.S. portfolio. What is the standard deviation of your portfolio?
a) 16.7% b) 15.5% c) 17.1% d) 18.6%

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beritop1089 beritop1089 · Answer 1 · 2019-12-07T08:10:20+01:00

Answer:

b) 15.5%

Explanation:

Let U.S. market portfolio be represented by variable "U"

And let Non- U.S. market portfolio be represented by variable "N"

σP = SQRT [ w²U*σ²U + w²N*σ²N + 2*wS* wN*σU*σN*correl. ]

whereby,

w= weight of...

σ² = variance of...

σP=SQRT[0.25²*0.182² + 0.75²*0.171² + 2*0.25* 0.75* 0.182* 0.171* 0.47 ]

σP = SQRT[ 0.002070+ 0.0164 + 0.005485]

= SQRT(0.023955)

= 0.15477 or 15.5%

= As a percentage, the standard deviation of your portfolio is 15.5%