In Figure 6.2, we have seen that th

In Figure 6.2, we have seen that the price that investors are willing to pay for a bond is mathematically linked to the rate of return that they receive. In fact, the orthodox theory of asset pricing says that it is the required rate of return that deter- mines the price that people are willing to pay. Formally speaking, the price that people are willing to pay is the value (more strictly, the present value) that they place upon
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Chapter 6 • The capital markets
the future payments. We look at how this is arrived at in the next few paragraphs. The theory and techniques that we draw upon are explained more fully in Appendix I: Portfolio theory. In the calculation of a present value for the future stream of income flowing from a bond, the size of the coupon payments will obviously be crucial. Other things being equal, a bond with a 15 per cent coupon will have a higher market price than one with a 10 per cent coupon. As a first attempt at a valuation we might be tempted simply to sum the future payments. However, this overlooks a fundamental prin- ciple of economics and finance, namely that a payment at some time in the future is worth less than the same payment now. This is not because of inflation (although the presence of inflation reinforces the point). Even in a zero-inflation world the principle would hold, as we explain in Appendix I: Portfolio theory. The reason that £5, say, today is worth more than £5 in a year’s time is that the £5 today could be put to some immediate use. Waiting for one year causes us a ‘loss’ equal to the pleasure, satisfaction or whatever which could have been enjoyed by using the £5 in the intervening year. The practice is therefore to discount future income payments by using a formula which takes the current rate of interest to represent the cost of waiting and recognises that the loss increases with the length of the wait. Notice that the rate of interest here is the nominal rate. Notice also that since its function is to represent the cost to us of not having the funds immediately available, it must be the rate of interest that could be earned in the market now on other assets of similar risk and duration to the bond. And this means that we can also think of it as the rate of return that we would require (since we can get it elsewhere) to induce us to hold the bond. (These equivalencies are discussed further in Appendix I: Portfolio theory.) Other things being equal, we should expect nominal interest rates to rise and fall with increases and decreases in the rate of inflation (i.e. we should expect real rates to be fairly stable). With high rates of inflation, therefore, we should expect high nominal interest rates. As we shall see, this will lower our present valuation of any future stream of income and explains why bond prices are sensitive to, among other things, expectations of inflation. The (discounted) present value of a payment in one year’s time is given by
C × (6.1)
where C is the coupon payment and i is the rate of interest. (Throughout our examples, we assume that bonds pay a single coupon, annually. In practice, many pay half the coupon at six-monthly intervals.) Take the case of the 15 per cent bond mentioned earlier. Assume that the next coupon payment is exactly a year away, and that interest rates are currently 10 per cent. The present value of the next coupon payment would be £15/(1 + 0.10) or £13.63. The value of the same payment in two years’ time is given by
C × (6.2)

Kết quả (Việt) 1:

Trong con số 6,2, chúng tôi đã thấy rằng giá nhà đầu tư sẵn sàng trả cho một mối quan hệ toán học được liên kết với tỷ lệ lợi nhuận mà họ nhận được. Trong thực tế, lý thuyết chính thống của tài sản giá cả nói rằng đó là yêu cầu tỷ lệ lợi nhuận mà ngăn chặn-mỏ mức giá mà mọi người sẵn sàng trả. Phát biểu chính thức, mức giá mà mọi người sẵn sàng trả là giá trị (chặt chẽ hơn, giá trị hiện nay) mà họ đặt trên167... ...Chương 6 • thủ đô thị trườngthe future payments. We look at how this is arrived at in the next few paragraphs. The theory and techniques that we draw upon are explained more fully in Appendix I: Portfolio theory. In the calculation of a present value for the future stream of income flowing from a bond, the size of the coupon payments will obviously be crucial. Other things being equal, a bond with a 15 per cent coupon will have a higher market price than one with a 10 per cent coupon. As a first attempt at a valuation we might be tempted simply to sum the future payments. However, this overlooks a fundamental prin- ciple of economics and finance, namely that a payment at some time in the future is worth less than the same payment now. This is not because of inflation (although the presence of inflation reinforces the point). Even in a zero-inflation world the principle would hold, as we explain in Appendix I: Portfolio theory. The reason that £5, say, today is worth more than £5 in a year’s time is that the £5 today could be put to some immediate use. Waiting for one year causes us a ‘loss’ equal to the pleasure, satisfaction or whatever which could have been enjoyed by using the £5 in the intervening year. The practice is therefore to discount future income payments by using a formula which takes the current rate of interest to represent the cost of waiting and recognises that the loss increases with the length of the wait. Notice that the rate of interest here is the nominal rate. Notice also that since its function is to represent the cost to us of not having the funds immediately available, it must be the rate of interest that could be earned in the market now on other assets of similar risk and duration to the bond. And this means that we can also think of it as the rate of return that we would require (since we can get it elsewhere) to induce us to hold the bond. (These equivalencies are discussed further in Appendix I: Portfolio theory.) Other things being equal, we should expect nominal interest rates to rise and fall with increases and decreases in the rate of inflation (i.e. we should expect real rates to be fairly stable). With high rates of inflation, therefore, we should expect high nominal interest rates. As we shall see, this will lower our present valuation of any future stream of income and explains why bond prices are sensitive to, among other things, expectations of inflation. The (discounted) present value of a payment in one year’s time is given byC × (6.1)nơi C là thanh toán phiếu giảm giá và tôi là tỷ lệ lãi suất. (Trong ví dụ của chúng tôi, chúng tôi giả định rằng trái phiếu trả tiền một phiếu giảm giá duy nhất, hàng năm. Trong thực tế, nhiều người phải trả một nửa các phiếu giảm giá tại khoảng thời gian 6 tháng.) Đi theo trường hợp của các trái phiếu 15 phần trăm đã đề cập trước đó. Giả định rằng các khoản thanh toán tiếp theo của phiếu giảm giá là chính xác một năm đi, và lãi suất tỷ giá hiện tại có 10 phần trăm. Giá trị hiện tại của các khoản thanh toán phiếu giảm giá tiếp theo sẽ là £15 / (1 + 0,10) hoặc £13.63. Giá trị của các khoản thanh toán tương tự trong thời gian hai năm được cho bởiC × (6.2)