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OLEGan [10]
3 years ago
7

Your investment portfolio consists of ​$15 comma 000 invested in only one stocklong dashAmazon. Suppose the​ risk-free rate is 5

%​, Amazon stock has an expected return of 12 % and a volatility of 40 %​, and the market portfolio has an expected return of 10 % and a volatility of 18 %. Under the CAPM​ assumptions, a. What alternative investment has the lowest possible volatility while having the same expected return as​ Amazon? What is the volatility of this​ investment? b. What investment has the highest possible expected return while having the same volatility as​ Amazon? What is the expected return of this​ investment? Hint​: Make sure to round all intermediate calculations to at least five decimal places.​
Business
1 answer:
Kay [80]3 years ago
8 0

Answer:

a)

The CAPM hypothesis states that the effective market is utilized place in the market and has the maximum eminent expected return of any assortment for a given randomness and the smallest variability for a assumed expected return. By allotment utilized place in the market assortment, you can achieve a standard return,

Thus,  

Expected Rate of Return = [Risk free Rate + Beta × (Market Risk - Risk free Rate)]

Beta = [Expected Rate of Return – Risk Free Rate] / [Market Risk - Risk free Rate]

Beta = [12% - 5%] / [10% -5%]

Beta = 7/5

Beta =1.4

The final possible instability while taking the same estimated rate of return as Amazon is $21,000 ($15,000 × 1.4) which indicate that it borrows $6,000 ($21,000 - $15,000). Now the -$6,000 is specified as strength benefit. So the volatility of the asset is,

Volatility = [Volatility of Asset x Beta]

Volatility = [18% × 1.4]

Volatility = 0.252 or 25.20%

Therefore the volatility is less than the volatility of Amazon.

b)

The market share has a instability of "n". The corresponding instability of Amazon will be 2.22 (40%/18%). So the assortment with the most notable predictable give back that has a faint variability from Amazon is $33,333.33 ($15,000x 2.22) which will be the market assortment and it also uses $18,333.33 ($33,333.33 - $15,000). Here the -$18,333.33 is specified as strength asset. So the return is,

Expected Return = [Risk free Rate + Beta × (Market Risk – Risk free Rate)]

Expected Return = [5%+ 122 × (10% - 5%)]

Expected Return = [5%+ 122 × 5%]

Expected Return = [0.05+0.111111]

Expected Return = 0.161111 or1 6.11%

Therefore the volatility is higher than the expected return of Amazon.

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3 years ago
Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 9.1% and 12.
podryga [215]

Answer:

A.) ALPHA

Portfolio A = 8.5%

Portflio B = 13.5%

B.) Sharpe measure

Portfolio A = 0.1519

Portflio B = 0.1479

Explanation:

T- bill rate (Rf) =5%

S&P 500 index ( Rm) = 10%

Portfolio A;

Expected rate of return = 9.1%

Beta (B) = 0.7

Standard deviation (s) = 27%

Portfolio B;

Expected rate of return = 12.1%

Beta (B) = 1.7

Standard deviation = 48%

Required rate of return for both portfolios;

Rf + B × (Rm - Rf)

Portfolio A :

5% + 0.7 ×(10% - 5%) = 5% + 0.7 × (5%)

5% + 3.5% = 8.5%

Portfolio B :

5% + 1.7 ×(10% - 5%) = 5% + 1.7 × (5%)

5% + 8.5% = 13.5%

A) Alpha(A) of Portfolio A and B ;

A = Expected return - Required return

Alpha of portfolio A :

9.1% - 8.5% = 0.6%

Alpha of Portfolio B:

12.1% - 13.5% = - 1.4%

B.) Sharpe measure for portfolio A and B;

Sharpe ratio = (Expected rate of return - Rf) / s

Portfolio A = (9.1% - 5%)/27% = 0.1519

Portfolio B = (12.1% - 5%)/48% = 0.1479

I will choose Portfolio A

8 0
4 years ago
Suppose that the risk-free rate is 5% and that the market risk premium is 7%. What is the required return on (1) the market, (2)
Nesterboy [21]

Answer:

1.

r market = 0.12 or 12%

2.

r stock = 0.12 or 12%

3.

r Stock = 0.169 or 16.9%

Explanation:

The required rate of return can be calculated using the CAPM or Capital asset pricing model equation. The formula for required rate of return under this model is,

r = rRF + Beta * rpM

Where,

  • rRF is the risk free rate
  • rpM is the risk premium on market
  • r represents the required rate of return

1.

The beta of the market is always considered to be 1. Thus, the required rate of return on market would be,

r market = 0.05 + 1 * 0.07

r market = 0.12 or 12%

2.

For a stock whose beta is 1.0, the required rate of return would be same as that for market. So, the required rate of return for a stock with a beta of 1.0 is,

r Stock = 0.05 + 1 * 0.07

r Stock = 0.12 or 12%

3.

The required rate of return for a stock with a beta of 1.7 is,

r Stock = 0.05 + 1.7 * 0.07

r Stock = 0.169 or 16.9%

3 0
3 years ago
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