Question

In: Finance

1. The following forecasts are available for the state of the economy and for two securities:...

1. The following forecasts are available for the state of the economy and for two securities:
a. Compute the two stocks expected return, variance, standard deviation, covariance and correlation.
b. Create a portfolio 30% in High Tech (remainder in Low Tech); calculate the portfolio expected return and standard deviation. Compare and discuss these results to Low Tech stand- alone results.

State of the Economy

 Probability of State Occurring Return on High Tech Asset (%) Return on Low Tech Asset (%)
Severe Recession 25.00% -30.00% 0.00%
Recession 25.00% -10.00% 8.00%
Normal Growth 25.00% 30.00% 12.00%
Boom 25.00% 50.00% 8.00%

Solutions

Expert Solution

a).

State of the Economy Probability of State Occurring (P) Return on High Tech Asset (%)
(Rht)		 Probability weighted return for High Tech Asset
(P*Rht)		 P*(Rht-E(Rht))^2
Severe Recession 25.00% -30.00% -7.50%                                0.0400
Recession 25.00% -10.00% -2.50%                                0.0100
Normal Growth 25.00% 30.00% 7.50%                                0.0100
Boom 25.00% 50.00% 12.50%                                0.0400
E(Rht) 10.00%
Variance (∑(P*(Rlt-E(Rlt))^2))                            0.100000
Stdev (Variance^0.5)                            0.316228
State of the Economy Probability of State Occurring (P) Return on Low Tech Asset (%)
(Rlt)		 Probability weighted return for Low Tech Asset
(P*Rlt)		 P*(Rlt-E(Rlt))^2 P*((Rht-E(Rht)*(Rlt-E(Rlt))
Severe Recession 25.00% 0.00% 0.00%                                0.0012                                          0.0070
Recession 25.00% 8.00% 2.00%                                0.0000                                        (0.0005)
Normal Growth 25.00% 12.00% 3.00%                                0.0006                                          0.0025
Boom 25.00% 8.00% 2.00%                                0.0000                                          0.0010
E(Rlt) 7.00% Covariance (∑P*((Rht-E(Rht)*(Rlt-E(Rlt)))
Variance (∑(P*(Rlt-E(Rlt))^2))                            0.001900                                     0.010000
Stdev (Variance^0.5)                            0.043589

Correlation = Covariance/StdevHT*StdevLT

= 0.0100/(0.316228*0.043589) = 72.55% (or 0.725476)

b). Portfolio expected return = (WHT*E(RHT))+(WLT*E(RLT))

= (0.3*10%)+(0.7*7%) = 7.90%

Portfolio standard deviation = [(WHT*StDevHT)^2 + (WLT*StDevLT)^2 + (2*WHT*WLT*Covariance)]^0.5

= [(0.3*0.316228)^2 + (0.7*0.043589)^2 + (2*0.3*0.7*0.01)]^0.5 = 0.1189

Compared to Low Tech stock, the portfolio has higher expected return but the riskiness has increased a bit.

jeff jeffy answered 1 year ago
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