## quant1 FRM level1

ps311088
Posts: 2
Joined: Sun Feb 22, 2015 11:13 am

### quant1 FRM level1

Variance of return of stockP=100
Variance of return of stockQ=225
Covariance of P&Q =53.2 at d end of1999 u r holding £4mn.u r considering a strategy of shifting £1mn into stockQ and keeping £3mn in stockP.what %of risk as measured by std deviation of return can be reduced by dis strategy???

edupristine
Finance Junkie
Posts: 946
Joined: Wed Apr 09, 2014 6:28 am

### quant1 FRM level1

The portfolio with 100% invested in Stock P has a variance of return equal to 100 and a standard deviation of return equal to 10.
Moving the portfolio to 75% (USD 3 million/USD 4 million) Stock P and 25% (USD 1 million/USD 4 million) Stock Q changes the variance to:
Variance = (0.75)^2 (100) + (0.25)^2 (225) + 2(0.75)(0.25)(53.2) = 56.25 + 14.06 + 19.95 = 90.26
Therefore, Standard deviation = (90.26) ^0.5 = 9.5
Hence, the percentage of risk reduced = (10-9.5)/10 = 5.0%.

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