Question

QUESTION 4

You are given the following data about expected returns on a Bank security on the LUSE where different states of the economy have the same probability of occurrence:

State                                           Return

Strong growth                              7.5%

Normal growth                             5.0%

Weak growth                                1.5%

Recession                                    -2.5%

Required:

Compute and fully interpret the following for the investment:

1. The Expected return for the security.

                                                                                             [5 Marks]

2. The volatility of the security returns using the standard deviation.

                                                                                             [6 Marks]

3. The Sharpe ratio of the banking security assuming a yield of 3.5% on a risk-free security.

                                                                                             [4 Marks]

4. Assuming you can only invest in one, which one of the two securities would you recommend to invest in and why?

                                                                                             [5 Marks]

Total 20 Marks

Answer 1

Solution Given State & Return (Rode Strong growth 75%. Narmal growth 5.0 weak growth lon ReceM100 -25) probability of occurance of each state = 25.4 @ Expected Return of - Z P*R Security notat (Rsec where p=probability R=Return (0.25 x 0.075]+[6.25 %0.05] + [0.25% 0.015] + [o:anx (-0.007 - = 0.01875 + 0.0125 + 0.00375 - 0.00625 0.02875 - 2.875-6

® co ) Standard & Deviation - Px R=R2? Blate R Ř IR Ř (R-8) 2 strong 7.5% 2.875 4.625 21.39 Nosimal 5.1 2.875 2.125 4.52 weak 1.57 2.9977-1-3761689 Recession -259 2.99 -345.78.39 standard Deviahona [0.25 21:39]+[0-35x4.52] J+ [0.25x1199) + (0-25 X28-89) - 5.348 + 1:13 +0.4725 ✓ + 7.22 p. 1732 = 3.765 0 Giaren Riskfree rate [RF] = 3.5% Sharpe statio = Rsee - Rf where Rsec = expected Rehern Rp = Risk free sale Osee - Standard deviation 001 volatality of security

sharp ratio = 2.875% -3.5.1 3.765 = -0.166 O Ö Sharpe oratio riefens to eatoa rietum econed from the security for the disk taken : In case order to invest is one security out of a two security, choose that Security having highest sharpe ration a ci) If Return, standard deviation of two Securities gives, then choose that security that gives highest Return with least lower standard deviation or equal standard Deviation coon opt for that Security having equal (Invost in) or highest Return having equal standard - deviations Note!- use markowrz model to determine foor investing in securities

Summary @ Expected Return of security = 2.875%. 6 volatality Steendeend deviation - 3.765 . © Sharpe ratio = – 0.166