Professor White, having reached the statutory retirement age, has retired and has been paid been paid...

Professor White, having reached the statutory retirement age, has retired and has been paid been paid his lump sum benefit of ₵200,000. The professor has no immediate need for the amount received and he is considering investing the amount in KK Motors Ltd, one of the top-performing stocks on the Ghana Stock Exchange. The stock under consideration has an expected return of 20% and a volatility of 12%. Suppose the risk-free rate is 15%, and the market portfolio has an expected return of 25% and a volatility of 18%. Illustrate numerically that given the market portfolio and the risk-free rate, an investment in the shares of KK Motors is not an efficient investment because: a. A combination of the risk free rate and the market portfolio will yield the same return as the investment in the stock of KK Motors Ltd, but with a lower risk. b. At combination of the risk free rate and the market portfolio offers the same level risk as the investment in the stock of KK Motors Ltd, but with a higher expected return.

Expert Solution


	Expected return of investment in KK motors	20%
	Risk (Standard Deviation) of returns in KK motors	12%

	R1=Expected Return of market portfolio=	25%
	S1=Standard deviation of return of market portfolio	18%
	R2=Return on investment in risk free rate	15%
	S2=Standard Deviation of investment in risk free rate	0%
	Cov(1,2) Covariance of return of market and risk free	0%
	w2=Proportion of investment in Market Portfolio
	w1=Proportion of investment in Risk free
	w1+w2=1
	Rp=Return of investment in combination of market and riskfree rate
	Vp=Variance of investment in market and risk free rate
	Rp=w1R1+w2R2=w125+w215
	Vp=(w1^2)(S1^2)+(w2^2)(S2^2)+2w1w2*Cov(1,2)
	Vp=(w1^2)(S1^2)=(w1^2)(12^2)=324*(w1^2)
	Sp=Standard Deviation of investment in market and Risk free rate
	Sp=Square Root(Vp)
	DIFFERENT COMBINATIONS OF MARKET PORTFOLIO AND RISK FREE

		w1	w2	Rp=25w1+15w2	Vp=324(w1^2)	Sp=SQRT(Vp)
		Market	Risk Free	Portfolio Return	Variance(%%)	Standard Deviation
		0	1	15.00%	0	0.00%
		0.1	0.9	16.00%	3.24	1.80%
		0.2	0.8	17.00%	12.96	3.60%
		0.3	0.7	18.00%	29.16	5.40%
		0.4	0.6	19.00%	51.84	7.20%
		0.5	0.5	20.00%	81	9.00%
		0.6	0.4	21.00%	116.64	10.80%
		0.6664	0.3336	21.66%	143.884823	12.00%
		0.7	0.3	22.00%	158.76	12.60%
		0.8	0.2	23.00%	207.36	14.40%
		0.9	0.1	24.00%	262.44	16.20%
		1	0	25.00%	324	18.00%
(a)	Investment of 50% in Market and 50% in Risk Free rate:
	Return =20% , Standard Deviation is lower at 9%

(b)	Investment of 66.64% in Market and 33.36% in Risk Free rate:
	Standard Deviation = 12% but return higher at 21.66%

jeff jeffy answered 1 year ago

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