Question

You are a wealth management analyst, and your first job is to make investment recommendations to a client.

After extensive research, you have narrowed down to the following two companies: XiG, pronounced as “eleven groceries”, is a grocery store chain operated in the U.S, with major competitor such as convenience store Seven-Eleven. XiG has very stable consumer base and its business is not very sensitive to the business cycle of the general economy.

TanW, acronym for Tan-my- way, is a beauty salon chain with a focus on tanning services. Its business is quite affected by the business cycle since people tend not to splurge on expensive non-necessities such as tanning spas.

Your client’s current portfolio has an expected return of 6% per year. Based on some economic models, you are confident to simplify the analysis as follows: Suppose there are five possible states of the economy each with equal probability. Here is a table of the returns (unit: %) corresponding to each state. This table facilitates your recommendation decisions:

States of Economy	XiG	TanW	Current
1	6	9	8
2	3	2	2
3	3	6	7
4	4	3	3
5	5	1	1

Which firm has a higher expected return and Which firm is riskier?

Answer 1

The five possible states of economy each, have equal probability, hence probability of each state of economy           = 100% / 5 = 20% or 0.20

1) Expected Return = P_i x X_i   (where P_i is probability of state of economy i and X_i is corresponding returns)

For company XiG = 0.20 x (6+3+3+4+5)% = 0.20 x 21% = 4.2 %

For company TanW = 0.20 x (9+2+6+3+1)% = 0.20 x 21% = 4.2 %

Hence, Both the firms have equal Expected Return.

2) Risk of Firms- We will measure risk by using the Standard Deviation of returns. Higher Standard Deviation indicates higher Risk.

Standard deviation for XiG = square root (0.20 x 6.8) = square root (1.36) = 1.167 % (rounded off)

Standard deviation for TanW = square root (0.20 x 42.8) = square root (8.56) = 2.926 % (rounded off)

Hence, firm TanW with higher Standard deviation is riskier.