Richard must decide how to allocate the capital in his portfolio. Richard has $5

Question

Richard must decide how to allocate the capital in his portfolio. Richard has $56,000 available to invest. He finds the rates of return for four stocks for the past 12 years and the results are given below. Richard plans to invest 25% of his funds in each stock.

a) How much will he invest in each stock?)

b) The expected value of Richard's porfolio is: (Round your answer to one one-hundreth of a percent)

c) The standard deviation of Richard's portfolio is: (Round your answer to one one-hundredth of a percent)

Year Stock A (%) Stock B (%) Stock C (%) Stock D (%)

-2.240

6.635

1 -5.450 -16.720 5.290

-2.240

Explanation / Answer

a) He will invest in each stock 25% of his funds in each stock.

that means he has $56,000 available to invest in four stocks,
i.e, Stock A = 56,000 * 25% = $14,000 and $14,000 each to stock B, stock C and stock D.

b) The expected value of Richard's porfolio is: 4.2%

Note: The mean return, in securities analysis, is the expected value, ormean, of all the likely returns of investments comprising a portfolio. It is also known as "expected return".

Formula for Expected value or return = (Sum of Average rate of return * weights i.e, allocation)

Sum of Average rate of return = total of all returns / 12years

stock A = 51.21 / 12 = 4.2675%

stock B = 147.3 / 12 = 12.275%

stock C = -29.304 / 12 = -2.442%

stock D = 31.11 / 12 = 2.5925%

Therefore expected return = (Average return of stock * 25%) + (Average return of stock B * 25%) + (Average return of stock C * 25%) + (Average return of stock D * 25%)

= (4.2675% * 25%) +(12.275%*25%) + (-2.442% * 25%) + (2.5925% * 25%)

=0.011 + 0.031 - 0.006 + 0.006

= 0.042

Therefore, expected return = 4.2%

Expected value = (Average return of stock * 25% of investment) + (Average return of stock B * 25% of investment) + (Average return of stock C * 25% of investment) + (Average return of stock D * 25% of investment)

= (4.2675% * 14,000) +(12.275%*14,000) + (-2.442% * 14,000) + (2.5925% * 14,000)

= 14,000 (4.2675% + 12.275% - 2.442% + 2.5925%)

=14,000 * 16.693%

Therefore, Expected value = $2,337.02

c) The standard deviation of Richard's portfolio is:

Standard deviation () is found by taking the square root of variance

formula for Variance = sum of weights (return - expected return)2

here er = expected return = 4.2%

The variance for Newco's stock is -0.026

Standard deviation () = square root of variance

=square root of -0.026 = 0.16

Therefore, Standard deviation () = 16%

Stocks Weights = w Average return = r Variance = w ( r-er)2 A 25% 4.2675% 0.25(4.2675% - 4.2%) = 0.017% B 25% 12.275% 0.25(12.275% - 4.2%)=2.019% C 25% -2.442% 0.25(-2.442% - 4.2%) = -1.66% D 25% 2.5925% 0.25(2.5925% - 4.2%) = -0.402 Variance = sum of weights (return - expected return)2 -0.026

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.