Question

You are currently only invested in the K Fund (aside from risk-free securities). The expected return for the K Fund is 13.50% with a volatility of 17.10%. Your broker suggests that you add Murni Berhad (MURNI) to your portfolio. With the volatility of 54%, MURNI has an expected return of 18.00%. There is a zero correlation between MURNI and K Fund. Currently, the Treasury Bill yields approximately 3.20%.

a) Show your working to prove whether your broker is right.

b) You follow your broker’s advice and make a substantial investment in MURNI stock so that, considering only your risky investments, 65% is in the K Fund and 35% is in MURNI stock. When you tell your finance lecturer about your investment, your lecturer says that you made a mistake and should reduce your investment in MURNI. Justify your opinion of whether your finance lecturer is right.

c) You decide to follow your finance lecturer’s advice and reduce your exposure to MURNI. Now MURNI represents 15% of your risky portfolio, with the rest in the K Fund. Decide and justify whether this is the correct amount of MURNI stock you should hold.

d) Calculate the Sharpe ratio of each of the three portfolios. Decide on the portfolio weight in MURNI stock that maximizes the Sharpe ratio.

Answer 1

a.

K Fund Return = 13.50%, Murni Fund Return = 54%

Just to check whether adding Murni fund will give more nreturns, lets construct portfolios with 0% of K fund to 100% of K fund and balance in MURNI fund. Both should add upto 100.

Portfolio return = Wa X Return from a + Wb x Return from B

The following table shows just by adding MURNI funds, returns improve more than 13.50% in a pure K Fund investment.

	Portfolio Weights	Return
K	0%	10%	20%	30%	40%	50%	60%	70%	80%	90%	100%	13.50%
Murni	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%	18%
Portfolio Returns	18.00%	17.55%	17.10%	16.65%	16.20%	15.75%	15.30%	14.85%	14.40%	13.95%	13.50%

2. Investment of 35% in Murni & 65% in K

Return from Murni = 18%, Return from K = 13.50%

Portfolio return = Wa X Return from a + Wb x Return from B

The portfolio return = 35% X 18% + 65% x 13.50% = 15.08%

One can counter the lecturer based only on returns that, any reduction in Murni, would also reduce portfolio returns.

	Portfolio Weights	Return	Volatility/ SD	Correlation
K	0%	10%	20%	30%	40%	50%	60%	70%	80%	90%	100%	13.50%	17.10%	0
Murni	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%	18%	54%
Portfolio Returns	18.00%	17.55%	17.10%	16.65%	16.20%	15.75%	15.30%	14.85%	14.40%	13.95%	13.50%

3. Following Lecturers advice, now investment in K is 85% & in Murni - 15%

Portfolio return = Wa X Return from a + Wb x Return from B

The portfolio return = 15% X 18% + 85% x 13.50% = 14.18%

One can clearly see, this return is less than 15.08% in the previous portfolio.

4. If we however, check the Sharpe Ratio, a measure of risk adjusted return, we will get a better investment.

Sharpe Ratio = (Returns from Portfolio - Risk Free Return) / Portfolio standard deviation

We will also need to calculate the Standard deviation of various portfolio

Standard Deviation of 2 stock portfolio

= (Wa ^2 x SDa ^2 + Wb^2 x SDb ^2 + 2 x Wa X Wb X SDa X SDb X Coefficient of Correlation)^ (1/2)

Where,

Wa = Weight of stock A in portfolio

Wb = Weight of stock B in portfolio

SDa = Standard Deviation of stock A

SDb = Standard Deviation of stock B

Coefficient of Correlation = Correlation between A & B

a. Portfolio of K : 65% & Murni : 35%

SD of K =17.10% & SD of Murni = 54% & Coefficient of Correlation = 0

Risk free rate = 3.20%

SD = [(0.65)^2 x (0.171)^2 + (0.35)^2 x (0.54)^2]^ 0.5 = 21.90%

REturn of this portfolio = 15.08%

Share Ratio = (15.08% - 3.2%) / 21.90% = 0.54

We can similarly calculate various scenarios of Portfolio in excel by introducing the formulas

	Portfolio Weights	Return	Volatility/ SD	Correlation
K	0%	10%	20%	30%	40%	50%	60%	70%	80%	90%	100%	65%	85%	13.50%	17.10%	0
Murni	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%	35%	15%	18%	54%
Portfolio Returns	18.00%	17.55%	17.10%	16.65%	16.20%	15.75%	15.30%	14.85%	14.40%	13.95%	13.50%	15.08%	14.18%
Portfolio SD	54.0%	48.6%	43.3%	38.1%	33.1%	28.3%	23.9%	20.1%	17.4%	16.3%	17.1%	21.9%	16.6%
Risk Free Rate	3.20%
Sharpe Ratio	0.27	0.30	0.32	0.35	0.39	0.44	0.51	0.58	0.64	0.66	0.60	0.54	0.66

From the above, it can be seen a portfolio of 85% in K & 15% in Murni is the best, maximising the Sharpe ratio