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5.2 THE EFFECTS OF AN INCREASE IN VOLATILITY

It is clear that the performance of the investment made according to an unlevered approach will offer more stable returns over time. By contrast, the volatility of returns will significantly increase or decrease as the level of leverage for the investment increases.

Figure 5.2 illustrates the impact of financial leverage on the volatility of returns. The analysis considers a hypothetical average unlevered total return of 9.5%, with volatility of

Volatility and returns on investment

FIGURE 5.2 Volatility and returns on investment

6.5%. The thick broken line represents a potential performance in returns which is in keeping with these assumptions. The broken lines represent the returns on the same investment made with financial leverage (debt to equity ratio) of respectively 50% and 75%, with debt servicing costs constant at 7%.

5.3 THE EFFECT OF FINANCIAL LEVERAGE ON RETURNS

The return on equity is a function of:

the LTV;

the spread between total return and debt servicing costs.

Figure 5.3 is based on the same assumptions as those listed in the first example involving positive financial leverage (unlevered total return of 9% and debt servicing costs of 7%). This ratio shows a progressive improvement of the return on equity due to the use of leverage.

For example, assuming a loan to value of 50%, the investment will generate the total return of 11% stated in the previous example.

Where loan to value exceeds 50%, the return on equity will increase quickly, whilst it will grow much more slowly if the LTV is less than 50%.

5.4 THE EFFECT OF FINANCIAL LEVERAGE ON RISK

Any increase to the return on an investment resulting from an increase in the LTV will be geometric. Similarly, the volatility of the investment will increase at a similar geometric rate, as illustrated by Figure 5.4.

Performance of equity return if the LTV changes

FIGURE 5.3 Performance of equity return if the LTV changes

Performance of risk against changes in the LTV

FIGURE 5.4 Performance of risk against changes in the LTV

For the purposes of this illustration, it has been assumed that the volatility of a debt-free investment (unlevered) is 8%. Consequently, the volatility of the levered equity return will be 16% with 50% leverage, and 32% with 75% loan to value. For LTVs lower than 50%, the impact of financial leverage on the volatility of equity return is essentially less incisive.

Leaving aside certain simplifications and the mathematical assumptions underlying Figure 5.4, the volatility of the investment doubles (compared to an equivalent debt-free investment) with a leverage of 50%, whilst it quadruples with a leverage of 75%.

 
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