Question

Tim Trepid is highly risk-averse while Mike Macho actually enjoys taking a risk.

a. Which one of the four investments should Tim choose? Compute coefficients of variation to help you in your choice.

Investments

Returns:

Expected Value

Standard Deviation

Buy stocks ..................................... \( 9,140 \) 6,140

Buy bonds ..................................... 7,680 2,560

Buy commodity futures ................. 19,100 26,700

Buy options ................................... 17,700 18,200

b. Which one of the four investments should Mike choose?

Short answer

a. Coefficient of variation
Buy stocks	0.6718
Buy bonds	0.333
Buy commodity futures	1.3980
Buy options	1.0282

Thus, Tim shall buy bonds because lower the coefficient of variation the better his risk- return trade off.

b. Mike should choose buying commodity futures.

Step-by-step solution

a.  Computation of coefficient of variation

$\begin{array}{c}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{variation}\mathbf{}\mathbf{Buy}\mathbf{}\mathbf{stocks}\mathbf{=}\frac{\mathrm{Standard}\mathrm{deviation}}{\mathrm{Expected}\mathrm{value}}\\ \mathbf{=}\frac{6140}{9140}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{6718}\end{array}$

a. Computation of coefficient of variation

a. Computation of coefficient of variation

$\begin{array}{c}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{variation}\mathbf{}\mathbf{Buy}\mathbf{}\mathbf{commodity}\mathbf{}\mathbf{futures}\mathbf{=}\frac{\mathrm{Standard}\mathrm{deviation}}{\mathrm{Expected}\mathrm{sales}}\\ \mathbf{=}\frac{26700}{19100}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{3980}\end{array}$

a. Computation of coefficient of variation

$\begin{array}{c}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{variation}\mathbf{}\mathbf{Buy}\mathbf{}\mathbf{options}\mathbf{=}\frac{\mathrm{Standard}\mathrm{deviation}}{\mathrm{Expected}\mathrm{sales}}\\ \mathbf{=}\frac{18200}{17700}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0282}\end{array}$

b. Investment decision

As Mike enjoys to take high risk, he will opt for purchase of commodity futures. The coefficient of variation of commodity future is higher in comparison to other options that means risk is comparatively higher.