### Abstract:

Fixed-income securities as an asset class form an integral part of investment
portfolios. Turnover in the South African bond market during 2009 was R13.4 trillion.
Normal coupon bonds are traded in the market on a yield-to-maturity basis, and the
price of the bond is calculated using a formula based on the sum of all the present
values of the future cash flows of the bond. The bond-pricing formula makes the
assumption that coupons can be reinvested at the same yield as the current yield-tomaturity.
If the investor invests the coupons at a different rate when coupons are paid
out, the investor will realise a different yield on the investment.
Interest rates are not static, but instead volatile, or change over time and maturity.
The term structure of interest rates are of a dynamic nature and the slope of the yield
curve changes as market forces impact on short-, medium- and long-term interest
rates. The bond-pricing formula ignores the term structure of interest rate. Bonds with
similar terms-to-maturity, trading at the same yield-to-maturity and different coupon
rates, will produce different returns to investors because of the reinvestment of the
coupons in the future.
Zero-volatility spreads are calculated by determining the present value of each
individual future cash flow of a bond at the relevant point on the yield curve. The sum
of all these present values is then compared to the price of the bond. The zerovolatility
spread will be equal to a fixed spread to the yield curve, and this will result in
the present value of future cash flows at the yield curve and the bond price being
equal to each other. Yield curves in this study are constructed as zero-coupon curves
with money market, FRA and swap rates as inputs to the calculation thereof.
Different methods of determining portfolio returns are investigated to enable the
researcher to distinguish between the returns of two bond portfolios.
Two portfolios with similar bonds with different zero-volatility spreads are compiled,
and similarities in bond portfolios are tested with price value of a basis point, duration
and convexity. The returns of these two portfolios are measured and compared over
the period 30 September 2000 to 30 November 2009 in order to determine whether
zero-volatility spreads as an evaluative tool can optimise bond portfolio returns.