Question

	Bonds	Equities
Expected Return	5%	12%
Expected Standard Deviation	10%	16%

1. Using the information above and given a correlation of 0.34 between the expected returns of Bonds and Equities, calculate the expected portfolio risk and return of an equally weighted portfolio of Bonds and Equities. Comment on the expected risk and return of the portfolio combining both asset types versus an investment in either bonds or equities.   (10 marks)

2. Comment on why diversification works, and describe different ways in which an investor may seek to diversify their portfolio.  (25 marks)

Answer 1

Part a) Portfolio expected return is calculated below:

Security	Weight	Return	Weighted return
Equity	0.5	12.00%	0.5 x 12 = 6.00%
Bonds	0.5	5.00%	0.5 x 5 = 2.50%
		Expected return	6+2.5 = 8.50%

$\sigma_{portfolio} = \sqrt{(W_{E} \sigma_{E})^{2} + (W_{B} \sigma_{B})^{2}+2 (W_{E} \sigma_{E}) (W_{B} \sigma_{B})\rho }$

• $\sigma_{portfolio} =$ portfolio standard deviation
• weight of equity
• weight of bonds
• $\rho =$ correlation

Diversification works because the assets are not perfectly correlated, like in this case the correlation between bonds and equity was 0.34. Therefore when the market condition is such that the equity is performing well, such as in boom, then that boosts the return however when market is doing badly, the fixed return of bonds reduces some of the poor effect of equity on the portfolio. If some assets are negatively correlated, the y add even greater diversification benefits. Further commodities protect the portfolio against inflation. So investors generally put various kinds of securities in the portfolio which have low or negative correlation to gain from the benefits of diverification.

• $\sigma_{E} =$ Standard deviation of equity
• $\sigma_{B} =$ Standard deviation of bonds

$\sigma_{portfolio} = \sqrt{(0.5 \times 10)^{2} + (0.5 \times 16)^{2}+2 (0.5 \times 0.5 \times 10 \times 16 \times 0.34)}$

$\sigma_{portfolio} = 10.78 \%$

• Return to Risk ratio of the portfolio= 8.5/10.78 = 0.79
• Return to Risk ratio of equity = 12/16= 0.75
• Return to Risk ratio of bond = 5/10= 0.50
• So combining the two in the portfolio produced higher return at a lower risk.