Understanding Interest Rates chapter 4 Understanding Interest Rates

Key points 1. yield to maturity 2. current yield 3. yield on a discount basis 4. return rate

4 types of credit instruments 1. Simple loan（普通贷款） In which the lender provides the borrower with an amount of funds, which must be repaid to the lender at the maturity date along with an additional payment for the interest. 2.Fixed-payment loan（ 固定支付贷款）（full amortized loan分期偿还债务） In which the lender provides the borrower with an amount of funds, which must be repaid by making the same payment every period.

3. Coupon bond（息票债券） In which pays the owner of the bond a fixed interest payment every year until the maturity date, when a specified final amount is repaid. Coupon rate 4. Discount bond （zero-coupon bond零息债券） Which is bought at a price below its face value, and the face value is repaid at the maturity date.

Present Value Concept of Present Value Simple loan of $1 at 10% interest Year 1 2 3 n $110 $121 $133 $100x(1 + i)n $1 PV of future $1 = (1 + i)n

Example What is the present value of $450 to be paid in 3 years if the interest rate is 20%? What is the present value of $250 to be paid in 2years if the interest rate is 15%?

Yield to Maturity: Loans Yield to maturity = interest rate that equates today’s value with present value of all future payments 1. Simple Loan (i = 10%) $100 = $110/(1 + i)  $110 – $100 $10 i = = = 0.10 = 10% $100 $100 2. Fixed Payment Loan (i = 12%) $126 $126 $126 $126 $1000 = + + + ... + (1+i) (1+i)2 (1+i)3 (1+i)25 FP FP FP FP LV = + + + ... + (1+i) (1+i)2 (1+i)3 (1+i)n

1. if you take out a loan from a bank, you need pay $900 as the yearly payment to the bank for 15 years, how much you borrowed from the bank? (an interest rate of 5%) 2. you decide to purchase a new house and need a $100,000 mortgage. You take out a loan from the bank that has an interest rate of 7%. What is the yearly payment to the bank to pay off the loan in twenty years?

Yield to Maturity: Bonds 3. Coupon Bond (Coupon rate = 10% = C/F) $100 $100 $100 $100 $1000 P = + + + ... + + (1+i) (1+i)2 (1+i)3 (1+i)10 (1+i)10 C C C C F P = + + + ... + + (1+i) (1+i)2 (1+i)3 (1+i)n (1+i)n Consol: Fixed coupon payments of $C forever C C P = i = i P 4. Discount Bond (P = $900, F = $1000) $1000 $900 = (1+i) $1000 – $900 i = = 0.111 = 11.1% $900 F – P i = P 

Relationship Between Price and Yield to Maturity Three Interesting Facts in Table 1 1. When bond is at par, yield equals coupon rate 2. Price and yield are negatively related 3. Yield greater than coupon rate when bond price is below par value

Coupon bond Write the formula of calculating the yield to maturity of a ten-year 8%coupon bond, face value is $3000, selling price is $2800. Find the price of a 10% coupon bond with a face value of $1000, a 12.25% yield to maturity, and eight years to maturity.

Yield on a Discount Basis Current Yield C ic = P Two Characteristics 1. Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond 2. Change in current yield always signals change in same direction as yield to maturity Yield on a Discount Basis (F – P) 360 idb = x F (number of days to maturity) One year bill, P = $900, F = $1000 $1000 – $900 360 idb = x =0.099 = 9.9% $1000 365 Two Characteristics 1. Understates yield to maturity; longer the maturity, greater is understatement 2. Change in discount yield always signals change in same direction as yield to maturity

Bond Page of the Newspaper

Distinction Between Interest Rates and Returns The rate of return is defined as the payments to the owner plus the change in its value, expressed as a fraction of its purchase price. Rate of Return C + Pt+1 – Pt RET = = ic + g Pt C where: ic = = current yield Pt Pt+1 – Pt g = = capital gain

Key facts about Relationship Between Interest Rates and Returns

Maturity and the Volatility of Bond Returns Key Findings from Table 2 1. Only bond whose return = yield is one with maturity = holding period 2. For bonds with maturity > holding period, i  P implying capital loss 3. Longer is maturity, greater is price change associated with interest rate change 4. Longer is maturity, more return changes with change in interest rate 5. Bond with high initial interest rate can still have negative return if i  Conclusion from Table 2 Analysis 1. Prices and returns more volatile for long-term bonds because have higher interest-rate risk 2. No interest-rate risk for any bond whose maturity equals holding period

Distinction Between Real and Nominal Interest Rates Real Interest Rate Interest rate that is adjusted for expected changes in the price level ir = i – e 1. Real interest rate more accurately reflects true cost of borrowing 2. When real rate is low, greater incentives to borrow and less to lend if i = 5% and e = 0% then: ir = 5% – 0% = 5% if i = 10% and e = 20% then ir = 10% – 20% = –10%

U.S. Real and Nominal Interest Rates

Questions And Problems 判断对错 1.到期日向债券持有人支付面值，而没有利息支付的债券被称为贴现债券。 T 2.出售价格低于面值的息票债券的到期收益率低于息票利率。 F 3.与10年内每年支付100美元的证券相比，你更愿意拥有10年底一次性支付1000美元的证券。

4.只要息票利率和债券价格一直，息票债券的到期收益率就可以计算出来。 F 5.当期收益率是对利率最精确的计量，当经济学家谈及利率是，所指的就是当期收益率。 6.如果利率从4%

4.What is the yield to maturity on a simple loan for $1 million that requires a repayment of $2 million in five years' time? 5.Which $1000 bond has the higher yield to maturity a 20-year bond selling for $800 with a current yield of 15% or a one-year bond selling for $800 with current yield of 5%? 6.You are offered two bonds, a one-year U.S. Treasury bond with a yield to maturity of 9% and a one-year U.S. Treasury bill with a yield on a discount basis of 8.9%.Which would you rather own?

7.Francine the Financial Adviser has just given you the following advice: “Long-term bonds are a great investment because their interest rate is over 20%.” Is Francine necessarily right? 8. Interest rates were lower in the mid-1980s than they were in the late 1970s, yet many economists have commented that real interest rates were actually much higher in the mid-1980s than in the late 1970s. Does this make sense? Do you think that these economists are right?