**WEDNESDAY: 15 December 2021.** **Time Allowed: 3 hours.**

**Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.**

**QUESTION ONE**

1. Explain the term “market portfolio”. (2 marks)

2. Benson Kilonzo is considering investing his funds equally in four different securities whose details are as indicated below:

**Security Expected return Variance Covariance**

** %** **%**

P 18 0.72 0.30

Q 16 0.4 0.35

R 10 0 0

Z 30 1.6 0.38

**Additional information:**

- The risk free rate of return is 10%.
- The expected rate of return of the market is 15%.
- The variance of the market is 20%.

**Required:**

The portfolio beta. (3 marks)

The required rate of return of the portfolio. (1 mark)

The required rate of return of each security and comment on its valuation. (5 marks)

3. Samuel Juma uses arbitrage pricing theory (APT) for evaluating investment strategies and from his earlier analysis, he knows’ that fund A and B shown below are well diversified and believes that an arbitrage opportunity exist for fund C. The expected return and factor sensitivities for the funds are shown below:

**Fund** **Expected return** **Factor sensitivity**

A 0.02 0.5

B 0.04 1.5

C 0.03 0.9

Further, Samuel Juma estimates the three funds sensitivity to inflation and Gross Domestic Product (GDP) growth. The information is presented below and he assumes a zero value for the error terms when working with the selected two factor model:

**Factor Sensitivity**

**Fund** **Expected return** **Inflation** **GDP growth rate**

A 0.02 0.5 1.0

B 0.04 1.6 0.0

C 0.03 1.0 1.1

The selected data on factor is provided below:

Factor **Forecasted value** **Actual value**

Inflation 2.0% 2.2%

GDP growth rate 1.5% 1.0%

**Required:**

Demonstrate how to exploit the arbitrage opportunity identified by Samuel Juma. (3 marks)

Determine which surprises has the greatest effect on fund returns. (3 marks)

Determine which fund is most sensitive to the combined surprises in inflation and GDP growth. (3 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Summarise five avenues for diversification in portfolio management. (5 marks)

2. The following information is provided on the market, risk free rate and two stocks A and 0:

** Expected return** **Correlation with market** **Standard deviation**

Treasury bill rate 4% 0.00 0.00

S & P 500 Index 11% 1.00 15.00

Stock A 14% 0.70 25.00

Stock 0 9% 0.40 20.00

**Required:**

Draw the capital market line (CML). (3 marks)

Calculate the betas of the stocks. (2 marks)

Plot the stocks relative to the CML and comment. (3 marks)

Calculate the alphas (a) of the stocks. (2 marks)

3. Benson Mwangi is considering two different portfolio strategies. The first is an active market timing trading strategy that is expected to yield a pretax return of 12%. All gains will be recognised each year and taxed at a short term capital gain rate of 5%. Alternatively, a less active tactical asset allocation trading strategy is expected to yield a pretax return of 18%. All gains will be recognised each year but will be taxed at 30%.

**Required:**

Using suitable computations, determine the strategy that is likely to produce a better after tax return. (3 marks)

Calculate the pretax return that is required on the market timing strategy to produce the same after tax return as the tactical asset allocation strategy. (2 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Evaluate four limitations of fundamental law of active management. (4 marks)

2. Cliford Kirwa and his wife Melisha Kirwa are planning for retirement and would like to compare the past performance of few mutual funds that they are considering for investment. They believe that a comparison over a five year period would be appropriate. They are given the following information about a superior fund they are considering:

**Year** **Assets under management (AUM) at** **Net return (%)**

** the beginning of year (Sh.”million”)**

1 30 15

2 45 -5

3 30 15

4 25 10

5 45 8

**Required:**

Calculate the money weighted rate of return (MWRR) of the fund (8 marks)

3. A portfolio manager has provided the following average portfolio and benchmark returns over the past 12 months:

Average portfolio return, **Rp** **= **0.0076

Average benchmark return, **RB** **= **0.0059

Standard deviation of the portfolio = 0.0063

**Required:**

The information ratio (IR) of the portfolio. (2 marks)

Interpret your results in (i) above. (2 marks)

4. Explain the following terms as used in portfolio management:

Crowdfunding. (2 marks)

Program trading. (2 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. Describe three methods that could be used in estimating value at risk (VaR) of a portfolio. (6 marks)

Explain the purpose of (VaR) in portfolio management. (2 marks)

2. Compare and contrast diversification of judgement” and “diversification of style” as used in portfolio management. (4 marks)

3. Robinson Murimi is managing a balanced portfolio of fixed income securities and equities securities worth Sh.1 million. The portfolio’s pretax expected return is 6.0%. The percentage of return composed of interest dividends and realised capital gain as well as the associated tax rates are listed below:

**Tax profile** **Annual distribution rate** **Tax rate**

Interest (i) **20%** 15%

Dividends (d) **30%** 5%

Capital gain (cg) **40%** 5%

Assume that the portfolio’s cost basis equals market value.

**Required:**

Calculate the expected future accumulation in15 years assuming these parameters hold for that time period. (5 marks)

4. The composition of the Fin Group Fund portfolio is as follows:

**Stock** **Number of shares** **Price (Sh.)**

**A** 200,000 35

B 300,000 40

C 400,000 20

D 600.000 25

The fund has not borrowed any funds, but its accrued management fee with the portfolio manager, currently totals Sh.3,000,000. There are 4,000,000 shares outstanding.

**Required:**

The net asset value (NAV) of the fund. (3 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Explain the following terms as used in behavioural finance:

Decision theory. (2 marks)

Bounded rationality. (2 marks)

Prospect theory. (2 marks)

Aversion to ambiguity bias. (2 marks)

Innumeracy bias. (2 marks)

2. Caroline Wekesa is a financial analyst at Wema Financial Services. She has been requested by her investment manager to develop an Investment Policy Statement (IPS) for a client.

Advise Caroline Wekesa on three roles of IPS in the portfolio management process. (6 marks)

3. Describe four reasons why it is important for portfolio managers to document information. (4 marks)

**(Total: 20 marks)**