Question

You invest in a mutual fund that charges a 3% front-end load, 1% total annual fees, and a 0.5% back-end load. How much will you pay in fees on a $15,000 investment that does not grow if you cash out after 5 years of no gain?

You invest in a mutual fund that charges a 3% front-end load, 1% total annual fees, and a 2% back-end load, which decreases .5% per year. How much will you pay in fees on a $10,000 investment that does not grow if you cash out after 3 years of no gain?

A stock has a correlation with the market of 0.53. The standard deviation of the market is 25%, and the standard deviation of the stock is 34%. What is the stock's beta?

A project has a 0.76 chance of doubling your investment in a year and a 0.24 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment? Report both answers in decimal form (Report 0.20 for 20%) with two decimal places each.

Answer 1

[1] Front-end load is paid at the time of purchasing the investment

front end load = purchase amount * front-end load , which is $15,000 * 3%, or $450

annual fees = average investment amount * annual fees, which is $15,000 * 1% or $150

total annual fees = $150 * 5 years, which is $750

back-end load = sale amount * back-end load, which is $15,000 * 0.5% , or $75

total fees = $450 + $750 + $75 ==> $1,275

[2] Year 1 : Beginning value = $10,000

Ending value = $10,000 - (0.5% * $10,000) ==> $9,950

annual fees = (($10,000 + $9,950) / 2)* 1% ==> $99.75

Year 2 : Beginning value = $9,950

Ending value = $9,950 - (0.5% of $9,950) ==> $9,900.25

annual fees = (($9,950 + $9900.25) / 2) * 1% ==> $99.25

Year 3 : Beginning value = $9,900.25

Ending value = $9,900.25 - (0.5% of $9,900.25) ==> $9,850.75

annual fees = (($9,900.25 + $9,850.75) / 2) * 1% ==> $98.76

front-end load = $10,000 * 3% ==> $300

back-end load = $9,850.75 * 2% ==> $197.02

total fees = $99.75 + $99.25 + $98.76 + $300 + $197.02 ==> $794.78

[3] Stock beta = (stock correlation with market) * (standard deviation of stock / standard deviation of market)

Stock beta = 0.53 * (0.34 / 0.25) ==> 0.72

[4] Expected return = (0.76 * 100%) + (0.24 * -50%) ==> 64%, or 0.64

variance = sum of squares of deviation from mean, weighted by probability

mean is expected return

Variance = (0.76*(1 - 0.64)^2) + (0.24*(0.50 - 0.64)^2)

Variance = 0.098496 + 0.004704 ==>  0.1032

Standard deviation = (0.1032 ^ 0.5) ==> 0.32