R = r + E(i)
5-5
Inflation-Protected Securities
5-6
Case
You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 7% and a 1-year “Inflation-Plus” CD offering 3.5% per year plus the rate of inflation. a. Which is the safer investment? b. Which offers the higher expected return? c. If you expect the rate of inflation to be 3% over the next year, which is the better investment? Why?
5-19
Key
D=6.279
D*=D/1+R=5.708 bond a,D*a= 8.080 bond b,D*b= 0.481 W×8.080+ (1- W)0.481=5.708 W=68.79%
• So for bond a: 760.608*68.79%= 523.23 for bond b: 760.608*(1- 68.79%)= 237.38
5-21
Bonds tips
• /bonds/12070870356 46.html • /sseportal/cn/zqpz/z q.shtml
5-22
• How to determine the yields at different time? • Buyers • Sellers • holders
5-18
Key :Cash outflow for lease company
T 1 2 3 … 15 total Cash flow 100 100 100 … 100 discount 90.909 82.645 75.131 … 23.939 760.608 0.12 0.109 0.099 … 0.031 1 weight 0.12 0.217 0.296 … 0.472 6.279
5-12
Duration
• Sensitivity of price to Return Rate • A bond with a duration of six years would be expected to fall 6% in price for every 1% increase in market interest rates
R(1− t) − i = (r + i)(1− t) − i = r(1− t) − it
5-8
Mini test
• Besides the risk-free interest rate,we need to add risk premium to determine the required rate of return of bonds. 1. How many kinds of risks can you tell ?(at least 4 types) 2. Make a list of rates that can help u to estimate the risks above?(at least 6 types,explain in detail)
5-20
Key
Liability liability previous New change 760.61 756.29 -4.32 Asset Long-term bond 523.23 519.03 -4.2 Short-term bond 237.38 237.26 -0.12
In case market interest rate rise to 10.1% from 10%, bond a yield becomes to 12.1%, bond b yield becomes to8.1%. The lease company can avoid rate risk
5-23
Spot rate
Sample Term Structure Spot Rate 11% 10% 9% 8% 7% 1 2 3 4 5 Term to Maturity (Years)
5-4
Equilibrium Nominal Rate of Interest
• As the inflation rate increases, investors will demand higher nominal rates of return • If E(i) denotes current expectations of inflation, then we get the Fisher Equation:
5-13
ti
Macaulay Duration (in periods) = t * PVCF + t * PVCF + ... + t * PVCF 1 1 2 2 n n
PVTCF
where t= period of cash flow i PVCF = present value of cash flow i PVTCF = present value of the total cash flow of the bond = price of the bond n = number of periods
5-9
The Components of an Investor’s Required Rate of Return
1.The Real Risk-Free Interest Rate 2. Inflation risk (CPI) 3. Liquidity risk (Spread,Turnover rate) 4. Default risk(credit rating) 5. Interest rate risk(duration) 6. recall risk 7. reinvestment risk 8. Currency risk 9. Political risk&event risity risk involves the ability to turn your investments into liquid cash in a short period of time. • Investors that don't learn to manage their liquidity risk could face bankruptcy even if they make a lot of money and have millions in net worth.
r = R −i
5-2
Equilibrium Real Rate of Interest
• Determined by: – Supply – Demand – Government actions – Expected rate of inflation
5-3
Figure 5.1 Determination of the Equilibrium Real Rate of Interest
5-14
Properties of the Macaulay Duration are
• The Macaulay Duration is always less than its maturity (except for a zero coupon bond, in which case it is equal to the time to maturity). • The greater the maturity, the greater the duration. • The lower the coupon, the greater the duration. • The greater the yield, the lower the duration.
5-17
Case study
• A lease company buys an equipment from Z company, promising to pay 1million ＄each year to Z company. At the same time, the lease company wants to invest 2 types of bonds, both are sold at par.Average interest rate is 10% : • a:Maturity 30years, coupon rate 12% • b:Maturity 6 months,yield 8% Question: how will the lease company do the investment to avoid rate risk?
CHAPTER 5
The valuation of riskless securities
5-1
Real and Nominal Rates of Interest
• Nominal interest rate – Growth rate of your money • Real interest rate – Growth rate of your purchasing power • If R is the nominal rate and r the real rate and i is the inflation rate:
5-7
Taxes and the Real Rate of Interest