CAIA Level II: Advanced Core Topics in Alternative Investments, 2nd Edition

34.3 VALUATION OF CONVERTIBLE SECURITIES

To identify convertible bond arbitrage opportunities, one must be able to calculate the fair value of a convertible bond.

34.3.1 Component Approach

The component approach is the most intuitive valuation approach for simple convertible bonds. It essentially divides the convertible bond into a straight bond component and a call option:

The straight bond component refers to the pure fixed-income portion of the convertible bond. It ignores the conversion possibility, and its value is easily obtained by discounting all future expected cash flows (coupons and final repayment) at an appropriate discount rate (the risk-free rate plus a credit spread). The discount rate of 8% is composed of a 4% risk-free rate added to the credit spread of 4%. Exhibit 34.2 illustrates the computation using a discount rate of 8% to calculate the total present value (PV) of the XYZ convertible bond as $760.44. Notice that the coupon rate of interest, 2%, is far below the discount rate of 8%. Issuing convertible bonds rather than straight debt reduces the current-year interest expense of the firm, as investors are willing to earn a lower coupon rate of interest in exchange for the value provided through the embedded equity call option.

EXHIBIT 34.2 Expected Cash Flow (CF) Decomposition for a Convertible Bond

This pure bond price is, in a sense, the minimum value of ...