Question

Suppose the security I and security J have the following historical returns:

Year	rI	rJ
2015	20%	40%
2016	29%	36%
2017	-12%	-25%

What is the standard deviation of the return on portfolio P? (Use n-1 for the denominator.)

		9.09%
		17.39%
		25.82%
		28.75%
		29.02%

Answer 1

SD of Portfolio = Sqrt { ( Wi * SD of I )^{2 +} ( Wj * SD of J )² + 2 * Wi * Wj * COV (I, J) }

SD of Sec = SQRT { sum [ X - AVg X ]² / n }

Computation of SD o I:-

AVg of I = (20% + 29% -12%) / 3

= 37% / 3 = 12.33%

SD of Sec = SQRT { sum [ X - AVg X ]² / n-1 }

= sqrt { 0.0929 / 2 }

= sqrt { 0.0464 )

= 0.2155 i,e 21.55%

Computation of SD o J:-

AVg of I = (40% + 36% -25%) / 3

= 51% / 3 = 17.00%

SD of Sec = SQRT { sum [ X - AVg X ]² / n-1 }

= sqrt { 0.2654 / 2 }

= sqrt { 0.1327 )

= 0.3643 i,e 36.43%

COV ( I,J) = { SUM [ ( I - Avg I ) * ( J - Avg J) ] } / n-1

COV ( I, J) = 0.1515 /2 = 0.07575

Portfolio SD = SQRT { (0.5 * 0.2155)² + (0.5 * 0.3643)² + 2 *0.5*0.5*0.07575 }

= SQRT { (0.10775)² + (0.18215)² + 0.0379 }

= SQRT { 0.01161 + 0.03318+ 0.0379 }

= SQRT { 0.08266}

=28.75%

Assumption : weights are rqual

pls comment if further assistance is required

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