What advantages do the mutual funds offer compared to the company stock?A Job at East Coast Yachts

You recently graduated from college and your job search led you to East Coast Yachts. Because you felt the company's business was

seaworthy, you accepted a job offer. The first day on the job, while you are finishing your employment paperwork, Dan Ervin, who works in

Finance, stops by to inform you about the company's $401(k)$ plan.

A $401($k$)$ plan is a retirement plan offered by many companies. Such plans are tax$-$deferred savings vehicles, meaning that any deposits you

make into the plan are deducted from your current pretax income, so no current taxes are paid on the money. For example, assume your

salary will be $$50,000$ per year. If you contribute $$3,000$ to the $401(k)$ plan, you will pay taxes on only $$47,000$ in income. There are also no

taxes paid on any capital gains or income while you are invested in the plan, but you do pay taxes when you withdraw money at retirement.

As is fairly common, the company also has a $5$ percent match. This means that the company will match your contribution up to $5$ percent of

your salary, but you must contribute the amount that you want matched, up to the maximum.

The $401($k$)$ plan has several options for investments, most of which are mutual funds. A mutual fund is a portfolio of assets. When you

purchase shares in a mutual fund, you are actually purchasing partial ownership of the fund's assets. The return of the fund is the weighted

average of the return of the assets owned by the fund, minus any expenses. The largest expense is typically the management fee, paid to the

fund manager. The management fee is compensation for the manager, who makes all of the investment decisions for the fund

East Coast Yachts uses Bledsoe Financial Services as its $401($k$)$ plan administrator. Here are the investment options offered for employees:

Company Stock One option in the $401($k$)$ plan is stock in East Coast Yachts. The company is currently privately held. However, when you

interviewed with the owner, Larissa Warren, she informed you the company was expected to go public in the next three to four years.

Until then, a company stock price is set each year by the board of directors.

Bledsoe S&P $500$ Index Fund This mu

Of the five mutual funds listed, rank them from high to low solely in terms of risk.

a$.$ Which fund is highest and why?

b$.$ Which fund is second highest and why?

c$.$ Subtract the return of the second highest fund from the highest fund. What does

this difference in return represent?

Suppose you decide to invest $$10,000$ of gross income $($i$.$e$.,$ pre$-$tax$)$ in the Bledsoe S&P

$500$ Index Fund and that the fund has an $11\mathrm{.}04\%$ annual return. Ignore any other taxes,

fees, issues, employer match, etc. not mentioned below.

a$.$ Assuming annual compounding, how much money will you have in ten years?

i$.$ Calculate the dollar amount assuming the initial investment is made with

pre$-$tax dollars.

Also, calculate the after$-$tax amount $($assume a $35\%$ tax rate on both

principal and capital gains$)$ in year ten.

ii$.$ Calculate the dollar amount assuming the initial investment is made with

after$-$tax dollars $($assume a $35\%$ tax rate$)$ and no taxes are deducted in year

ten.

Suppose you invest in the Bledsoe S&P $500$ Index Fund for ten years and earn a Holding

Period Return $($HPR$)$ of $184\mathrm{.}97\%.$

a$.$ What is your annual arithmetic return?

b$.$ What is your annual geometric return?

Calculate the Sharpe ratio for Bledsoe's S&P $500$ Index, Small$-$Cap, Large$-$Company

Stock, and Bond funds $($both net of expenses and ignoring expenses$).$ Assume a risk$-$free

rate of $0\mathrm{.}50\%.$

a$.$ Which fund has the highest Sharpe ratio $($ignoring expenses$)?$

b$.$ Which fund has the highest Sharpe ratio $($net of expenses$)?$

i$.$ What is the interpretation of this fund's ratio?

Assume the expected return for Bledsoe's Large$-$Company Stock Fund is $12\mathrm{.}15\%($with

standard deviation of $24\mathrm{.}43\%)$ and $6\mathrm{.}93\%$ for the Bond Fund $($with standard deviation of

$9\mathrm{.}96\%).$ You decide to allocate $80\%$ of your investment to the stock fund and $20\%$ to the

bond fund. Ignore expenses.

a$.$ What is your portfolio expected return?

b$.$ What is your portfolio standard deviation?

i$.$ Assuming correlation of $0\mathrm{.}75.$

ii$.$ Assuming correlation of $0.$

iii. Assuming correlation of $-0\mathrm{.}75.$

Calculate the Sharpe ratios for i$.,$ ii$.,$ and iii. $($ignore expenses and

assume a risk$-$free rate of $0\mathrm{.}50\%).$ Which portfolio was the highest?

If you were this new employee, what portfolio allocation would you choose and why?