Download MSF-CHP5

History of Interest Rates and
Risk Premiums
Chapter 5
McGraw-Hill/Irwin
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
INTEREST RATES
For the borrowers it is cost of borrowing
the funds.
For the suppliers, it is expected return
or required return from their
investments.
The demand and the supply of funds
determine the interest rates in the
market.
5-2
Real Rate of Interest
The rate that creates equilibrium btw
demand and supply of funds in a perfect
world where there is no inflation and no
liquidity preferences.
However economic conditions, trade
deficit or surplus, taxes etc. may change
the real rate of interest.
5-3
Nominal Rate of Interest
It is the actual rate of interest charged by
supplier and paid by demander.
It differs from the real rate of interest in two
factors;
1. Inflationary expectations
2. Liquidity preferences and other risk such as
default risk
R = r + IP + RP
Rf = r + IP
R = Rf + RP
5-4
Real and Nominal Interest Rates
Suppose 1 year ago you deposit $1000 in a 1 year
time deposit at a rate of 10%. At the end of the 1
year, you will get 1100$. Is a 100$ return for real?
This depends on “can you buy the things that you
could purchase a year ago”: It depends on your
purchasing power which is measured by Consumer
Price Index (CPI).
Suppose the rate of inflation (change in the CPI) is
6%.
So your purchasing power decreased by 6% a year.
Your net increase in your purchasing power is 4%
(10%-6%).
5-5
Real vs. Nominal Rates
If R is the nominal rate, r is the real rate, and i is the inflation
rate;
Real rate; r R-i
R= 0,10-0,06 =0,04
The exact relationship btw r and R is;
1 R
1 r 
1 i
Ri
.10  .6

 0.038  3.8%
1 i
1  .6
1+r: growth factor of your purchasing power
1+R: growth factor of your money
1+i: new price level
r
Empirical Relationship:
Inflation and interest rates move closely together
5-6
DETERMINANTS OF THE LEVEL OF INTEREST
RATES
Interest rates and their future expected values are the
important factors which effect our investment
decisions.
For exp. You have $10,000 in a savings account. The
bank pays you a variable int. rate which 30%. Also
you have an option of investing your money into longterm instrument (CDs).
Which financial instrument will you invest if you think
that the
Interest rate will decrase
Interest rate will increase
5-7
If you think that the int. rates will
decrease, you will want to invest into LT instrument with current higher rates.
If you think that the int. rates will
increase, you will want to invest into S-T
instruments.
5-8
Factors that effect the Interest Rates
However forecasting int. rates is not easy. We
have to understand the factors that effect the
rates and determine the level of int. rates:
The supply of funds from savers, primarily
households.
The demand of funds from businesses to invest in
plant and equipment.
The government’s net supply and demand of
funds.
5-9
The Equilibrium Real Rate of Interest Rate
Supply, demand of funds and government
actions determine the level of interest rates.
The supply curve slops upward because the
higher the real interest rate, the greater the
supply of household savings.
The demand curve slops downward because
the lower the int. rate, the more the
businesses will want to make investments in
capital goods.
Equilibrium is the point at which demand and
supply curve intersect, point E.
5-10
Government can shift these demand and
supply curves either to the right or to the left
through fiscal and monetary policies.
For. Exp. Government budget deficit
increases, increase the government
borrowing demand and shifts the demand
curve to the right, the new equilibrium point
will rise to E’. If we expect the govr. borrowing
increases, exp. future int. rates increase.
5-11
»Level of Interest Rates
Interest Rates
Supply
r1
r0
Demand
Q0 Q1
Funds
5-12
R  r  E (ri )
The Equilibrium Nominal Rate of Interest
As inflation rate increases, investors will demand
higher nominal rates of return on their investments. It
is necessary to maintain the expected real return
offered by an investment.
Fisher argued that “the nominal rate ought to
increase one for one with an increase in the expected
inflation rate”.
Fisher Equation;
R = r + Exp Inflation if r is stable.
However r is not stable. For exp. Return on L-T bonds
may include risk premium and r may vary.
5-13
Rates of Return: Single Period
P
1  P0  D1
HPR 
P0
HPR = Holding Period Return
P0 = Beginning price
P1 = Ending price
D1 = Dividend during period one
5-14
Rates of Return: Single Period Example
Ending Price =
Beginning Price =
Dividend =
48
40
2
HPR = (48 - 40 + 2 )/ (40) = 25%
5-15
E (r )   p( s)r ( s)
s
Probabilistic Data
There is uncertainty about the price of share a year
from now.
We can determine the probabilities about the state of
the economy and stock market and create scenarios.
E (r )   p( s)r ( s)
s
E®= Exp. rate of return,
p(s) = prob. Of each scenario,
r(s)= HPR in each scenario.
5-16
State of
Economy
Prob.
Ending
Price
HPR
Boom
0.25
$140
44%
Normal
0.50
110
14
Recession
0.25
80
-16
5-17
EXPECTED RETURN
Expected Return;
E (r )   p( s)r ( s)
s
E®= Exp. rate of return,
p(s) = prob. Of each scenario,
r(s)= HPR in each scenario.
E®= .25x44%+.50x14%+.25x(-16%) = 14%.
5-18
RISK
Variance and standard deviation;
 2   p( s)r ( s)  E (r )2
s
 2  .25(44%  14%) 2  .50(14%  14%) 2  .25(16% 14%) 2  450
  450  21.21%
5-19
Risk premium = exp HPR – Rf
Exp HPR= 14%, Rf = 6%
Risk premium = 14% - 6% = 8%
Real return = exp HPR – Inflation
premium
Excess Return = Actual return - Rf
5-20
2 
1 n
(rt  r ) 2

n  1 t 1
Historical data
E ( R) 
n
r
t 1
t
/n
n
1
2
2 
(
r

r
)

t
n  1 t 1
5-21
Annual Holding Period Returns (Arithmetic)
Geom.
Series Mean%
Sm Stk 11.6
Lg Stk 10.0
LT Gov
5.4
T-Bills
3.8
Inflation 3.1
Arith.
Mean%
17.7
12.0
5.7
3.8
3.1
Stan.
Dev.%
39.3
20.6
8.2
3.2
4.4
5-22
Risk Premiums-Real Returns
Risk
Series Premiums%
Sm Stk
13.9
(17.7-3.8)
Lg Stk
8.2
LT Gov
1.9
T-Bills
--Inflation
---
Real
Returns%
14.6
(17.7-3.1)
8.9
2.6
0.7
--5-23
PROBLEM 1
Using the historical risk premiums as
your guide, what would be your
estimate of the expected annual HPR
on the S&P 500 stock portfolio if the
current risk-free rate is 6%
5-24
SOLUTION 1
From Table 5.2, the average risk
premium for large-capitalization U.S.
stocks for the period 1926-2002 was:
(12%  3.8%) = 8.2% per year
Adding 8.2% to the 6% risk-free
interest rate, the expected annual
HPR for the S&P 500 stock portfolio is:
6.00% + 8.2% = 14.2%
5-25
Real vs. Nominal Risk
Zero-coupon bond that pays $1000 on its
maturity date, 20 years from now. Price of the
bond $103.67, nominal rate 12% per year.
Compute the real annualised HPR for each
inflation rates; a) 12%, b) 4%
a) Inf. Rate: 12%: the purchasing power of
$1000 to be received in 20 years= $103.67
which is the current price of the bond so that
HPR= 0.
5-26
Inf. Rate: i= 4%
Purchasing Power= $1000/(1+i)n =
$1000/(1+0.04)20 = $456.39.
Real HPR;
1 R
1.12
r
1 
 1  7.69%
1 i
1.04
5-27
PROBLEM 2
During the period of severe inflation, a
bond offered a nominal HPR of 80% per
year. The inflation rate was 70% per
year.
A) What was the real HPR on the bond
over the year?
B) Compare this real HPR to the
approximation r = R - i
5-28
SOLUTION 2
a r  1  R  1  R  i  0.80  0.70  0.0588  5.88%
1 i
1 i
1.70
b. r  R  i = 80%  70% = 10%
Clearly, the approximation gives a
real HPR that is too high.
5-29
PROBLEM 3
You are considering the choice btw 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?
5-30
SOLUTION 3
a. The “Inflation-Plus” CD is the safer
investment because it guarantees the
purchasing power of the investment.
Using the approximation that the real
rate equals the nominal rate minus the
inflation rate, the CD provides a real
rate of 3.5% regardless of the inflation
rate.
5-31
b. The expected return depends on the
expected rate of inflation over the next
year. If the expected rate of inflation is
less than 3.5% then the conventional
CD offers a higher real return than the
Inflation-Plus CD; if the expected rate of
inflation is greater than 3.5%, then the
opposite is true.
5-32
c. If you expect the rate of inflation to be 3%
over the next year, then the conventional CD
offers you an expected real rate of return of
4%, which is 0.5% higher than the real rate
on the inflation-protected CD. But unless you
know that inflation will be 3% with certainty,
the conventional CD is also riskier. The
question of which is the better investment
then depends on your attitude towards risk
versus return. You might choose to diversify
and invest part of your funds in each.
5-33
PROBLEM 4
Bear
Prob.
.2
Stock A -20%
Stock B -15%
Market Conditions
Normal
.5
18%
20%
Bull
.3
50%
10%
A) What are the expected returns for Stock A&B.
B) What are the standard deviations of returns
on Stocks A& B?
5-34
E(RA)= O.2x(-20%)+0.5x(18%)+0.3x(50%)
= 20%
E(RB)= 10%
A2  0.2(20%  20%) 2  0.5(18%  20%) 2  0.3(50%  20%) 2  576
A  24%
B  13%
5-35
PROBLEM 5
Assume that of your $10,000 portfolio ,
you invest $9,000 in Stock A and $1000
in Stock B (Problem 3). What is the
expected return on your portfolio?
5-36
SOLUTION 5
E(RP) = 20%x0.90 + 10%x0.10 = 19%
5-37
Homework 1:
Please select 5 stocks which are traded
at ISE (Istanbul Stock Exchange). Find
their monthly returns for the past five
years. (Jan 2007- Dec 2011) from the
web page of ISE (imkb.gov.tr or
ise.gov.tr). Calcuate their aritmetic
average, geometric average and
standard deviations by using excell.
(Please consider the TL based returns)
5-38