Mutual Funds

Mutual Funds 1

Mutual Funds

Name:

Institution:

Mutual Funds 2

Problem 1

You purchased 1,000 shares of the New Fund at a price of $20 per share at the beginning of the

year. You paid a front-end load of 4.25%. The securities in which the fund invests increase in

value by 16.75% during the year. The fund's expense ratio is 1.20%. What is your rate of return

on the fund if you sell your shares at the end of the year?

Solution

Cost of shares = Pₒ = (NAVₒ × Shares) ÷ (1 - FL)

= ($20 × 1,000) ÷ (1 -0.0425) = $20,888

NAV₁ = NAVₒ (1 + Invest. Return - Expense ratio)

= $20(1 + 0.1675 – 0.012) = $23.11

Therefore, at time 1 the value of 1,000 shares = $23,110

Due to front end load, Pₒ ≠ NAVₒ but, due to lack of back end load, P₁ = NAV₁

We calculate return from prices: R = P₁ ÷ Pₒ - 1

= ($23,110/$20,888) - 1 = 10.64%

Problem 2

The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-

year price depend on the state of the economy by the end of the year as follows:

Mutual Funds 3

Dividend

Stock Price

Boom

$2.50

$50

Normal economy

$1.00

$43

Recession

$0.75

$34

Calculate the expected holding-period return and standard deviation of the holding-period return.

All three scenarios are equally likely.

Solution

Holding-period return

Boom = ($50 - $40 + $2.50) ÷ $40 = 31.25%

Normal = ($43 - $40 + $1) ÷ $40 = 10%

Recession = ($34 - $40 + $0.75) ÷ $40 = -13.13%

(1/3 × 31.25%) + (1/3 × 10%) + (1/3 × -13.13%) = 9.34%

1/3(31.25 – 9.34) ^2 + 1/3(10 – 9.34) ^2 + 1/3(-13.13 – 9.34) ^2 = 328.51 Variance

Square root of 328.51 = 18.12 Standard Deviation

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