# Yield to maturity is what drives the bond market

The term yield essentially refers to the return from a security. The return from a bond is also referred to as its yield, and yield to maturity is a commonly reported, yet largely misunderstood term. The yield to maturity is the discount rate that makes the present value of all the cash flows from the bond equal to its current market price.

The term price refers to the dirty price of the bond, that is, the sum of its clean price and accrued interest. To actually earn the computed yield to maturity, the investor must satisfy two conditions. First, he must hold the bond till maturity, and second, he must re-invest all intermediate cash flows at the yield to maturity itself.

Yield to maturity (YTM) is the internal rate of return (IRR) of the bond. The IRR of a project is the discount rate that equates the present value of future cash flows to the initial investment. In capital budgeting parlance, it is that discount rate that makes the net present value (NPV) equal to zero. A bond is also like a project because we make an investment at the outset and take back cash flows subsequently. It is just that the IRR of a project is termed as its YTM.

Projects in real life can be complex. In some cases they may give rise to what are termed as mixed cash flows. That is an initial investment may be followed by further investments interspersed with cash inflows, at subsequent points in time. The problem with such cash flow streams is that they may lead to multiple real positive IRRs, all of which are technically correct.

In this case, if the cost of capital is less than 15%, or greater than 28%, then the inference is clear cut. But what if the cost of capital is 20% The first IRR would say that the project should be rejected, while the second would would cause us to conclude that the venture is acceptable. Since both IRRs are mathematically valid, this dilemma is difficult to resolve. Fortunately in the case of the YTM, a bond has what are termed as pure cash flows.

A bond holder receives income from three sources. First, he gets periodic interest or coupon payments. Second, he can earn interest by reinvesting these coupons. Since coupons themselves represent interest, the second source of income may be perceived as interest on interest. Finally, at the time of maturity he will earn income in terms of the face value. A proper yield calculation ought to factor in all three sources of income. The YTM statistic does so. But it makes two key assumptions.

The first is that the bond will be held to maturity and that consequently the investor will receive all the projected cash flows. The second is that all intermediate coupons will be re-invested at the YTM itself, whatever that value may be. The second assumption is essential for us to obtain a compounded periodic return equal to the YTM over the life of the bond. The YTM is therefore termed as a promised yield, for if either of the conditions were to be violated, the investor will not earn what he is anticipating.

One of the risks in a bond is that cash flows may subsequently have to be reinvested at rates that are less than the calculated YTM. This is termed as re-investment risk. This can be accounted for in practice by assuming a rate at which each intermediate cash flow is re-invested. Such a yield statistic is termed as the realised compound yield (RCY). This measure may be computed on an ex-ante or on an ex-post basis. In the first case we would actually assume rates of re-investment for each cash flow. The practice is that we assume that every cash flow will be reinvested at the same rate.

There is another statistic from a return standpoint known as the horizon or holding period yield. It too assumes that every cash flow is reinvested at a specified rate and hence is similar to the RCY. However, in this case we need not assume that the bond is held to maturity. A consequence of the second assumption is that the bond will have to be valued at the time of sale. Once again this yield can be computed either on an ex-ante or on an ex-post basis.

The writer is author of Fundamentals of Financial Instruments, published by Wiley, India