Question

You are working as head of the investment section at a very important firm in the financial sector. Unfortunately, the rest of the management team, and the board, missed the second module “Market failures and resource allocation” and you therefore need to clearly motivate your choices for the firm’s account. The options the board would like you to rank are the following: (1) Keep 10 000 SEK in the firms vault, or (2) Buy a risk free Government Bond with a return of 310 SEK per year forever, or (3) Buy shares of another firm (called X) on the stock market to be sold after one year. The selling price after one year is uncertain. The estimated probability is 50% for a future value of 15 000 SEK and 50% for a future value of 6630 SEK. (4) Buy shares of another firm (called Y) on the stock market to be sold after two years. The selling price after two years is uncertain. The estimated probability is 50% for a future value of 15 000 SEK and 50% for a future value of 6630 SEK. The relevant real interest is assumed to be 3% and the board of your firm is risk neutral. a) Rank the options and explain to the board (and me) how you think firm should act. b) Calculate the standard deviation (where it is relevant) and discuss in terms of uncertainty.

Answer 1

The four options are presented to invest the idle cash which could generate extra return for the company.

a) We will look at each option

1) The option of keeping cash will not yield any gain and inflation will erode the value of that cash.
The cash will generate 0% return or probably -3% in terms of value after a year.

2) The investment in bond will yield the payment of SEK 310 forever. This is a perpetual bond.

Rate of return = (Final Value / Initial Value) - 1
310 / 10000
= 0.0310 or 3.10%

This is marginally higher than the real interest rate.

3) The stock X is expected to be SEK 15000 or SEK 6630 with 50% probability of each event.

(15000 / 10000) - 1 = 0.5 or 50%

(6630 / 10000) - 1 = -0.337 or -33.7%

We will calculate the expected return with probability

(0.5 * 50%) + (-33.7% * 0.5)
= 0.25 + (-0.1685)
= 0.0815 or 8.15%

4) The data about the stock Y is also same here but it is sold after two years

((15000 / 10000) ^ 0.5) - 1 = 0.2247 or 22.47%

((6630 / 10000) ^ 0.5) -1 = -0.1858 or -18.58%

Expected Return
(0.5 * 0.2247) + (-0.1858 * 0.5) = 0.0195 or 1.95%

We could see that the option 1 and 4 are below the acceptable rate of 3%.

Option 2 is slightly positive but option 3 of investment in stock X is the only favorable here.

b) Standard deviation is only subjected to investment in stock X and Y

Stock X

Mean
(50 - 33.7) / 2 = 8.15

((50 - 8.15) ^ 2 + (-33.7 - 8.15) ^ 2) / 2)
= 1751.4225

This is variance and we will take a square root of it to calculate the standard deviation

1751.4225 ^ 0.5 = 41.85%

Stock Y

Mean = (22.47- 18.58) / 2
= 1.945

Variance =
((22.47 - 1.945) ^ 2 + (-18.58 - 1.945) ^ 2) / 2)
= 421.2756

Standard Deviation = 421.2756 ^ 0.5
= 20.525