You have $100 to invest in a portfolio. The portfolio is composed of a risky asset...

Free

90.2K

Verified Solution

Question

Finance

You have $100 to invest in a portfolio. The portfolio iscomposed of a risky asset with an expected rate of return of 12percent and a standard deviation of 15 percent and a Treasury billwith a rate of return of 5 percent. What percentage of your moneyshould be invested in the risky asset to form a portfolio with anexpected rate of return of 9 percent?

Answer & Explanation Solved by verified expert

4.2 Ratings (894 Votes)


Risky Asset=Asset 1 Treasury Bill=Asset 2
Return of asset1=R1=	12%
Return of asset2=R2=	5%
Standard deviation of asset 1=S1	15%
Standard deviation of asset 2=S2	0
Covariance(1,2)=	0
w1=Investment in asset 1
w2=Investment in asset 2
Portfolio Return=Rp
w1R1+w2R2=w112+w25			……..Equation (1)
Vp=Portfolio Variance=(w1^2)(S1^2)+(w2^2)(S2^2)+2w1w2*Cov(1,2)
Portfolio Variance=(w1^2)(15^2)+(w2^2)0+2w1w2*0
Vp=Portfolio Variance=(w1^2)*225……………Equation (2)
Portfolio Standard Deviation=Square root of Variance

	w1	w2	Rp=w112+w25	Vp=(w1^2)*225	Sp=Square root of Vp
	Weight of	Weight of	Portfolio	portfolio	Portfolio
	Risky Asset	T-Bill	Return(%)	Variance	Std. Deviation(%)
	0	1	5	0	0
	0.1	0.9	5.7	2.25	1.5
	0.2	0.8	6.4	9	3
	0.3	0.7	7.1	20.25	4.5
	0.4	0.6	7.8	36	6
	0.5	0.5	8.5	56.25	7.5
	0.5714	0.4286	8.9998	73.462	8.571
	0.6	0.4	9.2	81	9
	0.7	0.3	9.9	110.25	10.5
	0.8	0.2	10.6	144	12
	0.9	0.1	11.3	182.25	13.5
	1	0	12	225	15

Investment in RISKY ASSET	$57.14	(0.5714*100)
Investment in TREASURY BILLS	$42.86	(0.4286*100)
Standard Deviation of the Portfolio	8.571	%

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member

Transcribed Image Text

You have $100 to invest in a portfolio. The portfolio iscomposed of a risky asset with an expected rate of return of 12percent and a standard deviation of 15 percent and a Treasury billwith a rate of return of 5 percent. What percentage of your moneyshould be invested in the risky asset to form a portfolio with anexpected rate of return of 9 percent?

You have $100 to invest in a portfolio. The portfolio is composed of a risky asset...

Free

90.2K

Verified Solution

Question

Finance

Answer & Explanation Solved by verified expert

Get Answers to Unlimited Questions

Membership Benefits:

Transcribed Image Text

Other questions asked by students