48323566 introduction to investment analysis rates of return
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Introduction to Investment
Analysis
Rates of Return
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Investment Return
Investment Horizon or Holding Period is the
period between the purchase and sale date.
How do you know how well an investment hasdone?
Ans. You calculate the rate of return
Historical rates of return are used to develop an
estimate of the expected rate of reurn
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Components of Investment Return
1. Current Income is the periodic income that aninvestment generates.
a) Interest for bonds
b) Dividends for stocks
c) Rent for real estate
To be considered income, it must be received in
the form of cash or be readily convertible intocash
2. Capital Gains (Loss) = appreciation or
increase (Decrease) in value of the investment.
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Total Return
Total return in Dirham =Current Income +
Capital Gains
Never compare two investments based on thetotal return in Dirhams. Instead use the rate
of return
InvestmentInitialturnTotalr Re
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Holding Period Return
V1= The market value of the portfolio at the end of the interval.
V0= The market value of the portfolio at the begging of the interval
Cash Flow = cash distribution to the investor
Dividends in the case of Stocks
Interest in the case of Bonds
Rent in the case of Real Estate
0
01)(
V
VVFlowCashR
p
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Investment Return
0
)01
(
0
)(
0
01
V
VV
V
FlowCash
pR
V
VVFlowCashR
p
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Investment Return
HPR =
Dividend Yield + Capital Gains Yieldin the case of Stocks
Current Yield + Capital Gains Yieldin the case of bonds
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Holding Period Returns
Can be calculated for any investment horizon
We can calculate six-month holding period return
or a one year holding period returnHowever, we can only compare holding period
returns for similar holding periods.
A one year HPR can only be compared with one
year HPR. A six-month HPR can only be
compared with a six-month HPR.
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Understanding Return Components
Current income is realized return because theinvestor generally receives current income duringthe period.
Capital gains (losses) may or may not be realized.
Capital gains (losses) are realized only if theinvestment is sold at the end of the holding period.
If the investment is not sold at the end of the holdingperiod, then any gains(losses) are unrealizedgains(losses) also called paper gains (losses).
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Understanding Return Components
Both current income and capital gains may be
negative.
Any investment in Stocks, Bonds, or Real Estatemay result in capital loss.
But how would a current income be negative?
An investor may have to pay out more than he
receives from an investment. Occurs mostly with real
estate investments when the rent is less than the
associated payments of maintenance, for example.
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How to compare investments
with different time horizons?
We bring both investments to a common
denominator. The best way is to annualize
the returns.
Mistake at the bottom of page 9 and top of
page 10.
periodholdingainyearsofnumbertheisnwhere
H PRAHPR n
""
1)1(1
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Calculate the Mean historical rates of return
A security may have achieved different
rates of return over a number of years.
We need a summary measure that would
indicate the investments typical
performance.
Two summary measures are availableArithmetic Mean and Geometric Mean
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Arithmetic Mean
The Formula for the Arithmetic Mean is:
The Formula for the Geometric Mean is,
The Geometric Mean measures the compoundrate of growth of the initial portfolio during the
period.
n
H PRMeanArithmetic
1)1(1
nH PRMeanGeometric productmeans
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Comparison of the Geometric
and the Arithmetic Mean
The Arithmetic mean Geometric mean
The only time they are equal is when the returns
are identical.When do we use each method?
Use the geometric mean when Use the geometric average if you are concerned with long-term
performance, as are a lot of investors. It is the better measure ofreturn because it measures the compound measure of return.
When we wish to estimate the ending value of an investment overa multi-period horizon conditioned on past experience. i.e., toestimate the future value based on past experience.
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Comparison of the Geometric
and the Arithmetic Mean
The Arithmetic mean provides a good indication
of what would be the next years expected rate of
return. It is our best guess of the HPR in a givenyear.
It overestimates the assets long-run
performance.
The difference between the arithmetic and the
geometric rates will increase as the variability of
the holding period returns increases.
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Risk and Return
Realized return is the return that was earned.
Expected return is an estimated return thatinvestors anticipate over some period. It is subjectto uncertainty and may not occur.
Investors like to maximize expected returns subjectto some constraints. Risk is the primary constraint.
People dont make their decisions based only onreturn. They need to take risk into consideration.
Risk is the chance that the actual return of aninvestment will differ from the expected outcome.
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Risk and Return
Risk is associated with the dispersion in
the likely outcomes. If an asset has no
variability, it has no risk.The most common form of dispersion is
the standard deviation of return. The
higher the value of the standard deviation,the more dispersion and the riskier the
investment is.
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Required rate of return
When selecting securities we have to find onethat provides a rate of return that compensates usfor three things:
The Time Value of Money
The expected rate of inflation
The risk involved
Also called the discount rate. It is the rate that the investors require if the
investor is to invest in a particular security.
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Required rate of return
The required rate of return
The real risk free rate is the basic interest rate, assumingno inflation and no uncertainty about future cash flows.The only sacrifice was deferring using the money for a
period of time.
An investor in an inflation-free economy who knew withcertainty what cash flows he/she would receive at whattime would demand the real-risk free rate on an
investment. The only sacrifice was deferring using themoney for a period of time, i.e., deferring consumption.
pemiumInflationrateFreeRiskalralNo
emiumRiskemiumInflationratefreeriskalr
f
Remin
PrPrRe
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What influences the risk free rate?
Q: What influences people to postponeconsumption. This depends on:
1. Time preference of individuals. Since this varies for investors, the
market creates a composite rate that includes the preference of allinvestors.
This composite changes over time but it is a gradual change sinceall investors in the economy influence it.
The changes in consumption preferences might be offset by thechanges in different set of investors
2. The set of investment opportunities available in the economy and isdetermined by the long-run real growth rate in the economy.
A rapidly growing economy has more investment opportunities toinvest the funds and experience positive rates of return.
Those looking to invest in a rapidly growing economy would
require a higher rate of return and those looking for funds areready to pay a higher rate because of the growth.
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Investing contains risk
Required rate of return will be composed of twoelements:
1. A real risk free rate
2. A risk premium to compensate for the added risktaken
Purchasing any security (financial instrument)has risk.
Investors are risk-averse. They are not willingto take on more risk unless they arecompensated with extra return. The higher therisk of the security the higher will be therequired rate of return.
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Purchasing Power Risk (Inflation Risk)
As an investor you would like to get back yourmoney plus some form of current income and/orcapital gains.
If your HPR over a seven-year period was 80%,are you better off??
The answer really depends on inflation (level ofprices) experienced over the same period. If
inflation went up by 100%, then clearly you areworse off.
You are worse off because the investor is clearlyreceiving an amount that is lesser in value than the
one originally invested.
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Inflation reduces the purchasing
power of investment returns
If a bank advertises 7% on its savings account,
the advertised amount is the nominal rate of
return; they are not adjusted for inflation.You are better off in purchasing power terms if
the nominal return is more than the inflation rate.
If your return over a year, 15% when the rate of
inflation over the same period was 10%, the
portfolios real rate of return is approximately
rateInflationratealNoreturnofrateal minRe
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Real rate of return
Real rate of return = 15%-10%=5%
The investor is better off by 5% in real
terms (purchasing power terms).
From the 15% gain, 10% has been lost to
inflation. 5% results in real gain, which is
increased consumption.
The exact real rate of return formula is:
1
inf1
min1Re
ratelation
ratealNoreturnrateal
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Real Rate of return
If an investors portfolio had a return of 8% whenthe rate of inflation was 10%, then the rate ofreturn is approximately2%. The only sacrifice
was deferring using the money for a period oftime.
Q: Would our investor have been better offwithout that investment; that is left his money incash?
A: Clearly No. Had our investor left his moneyin cash, the nominal rate = 0 and the real ratewould have been 0% -10% = -10% which is wayworse that2%.
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Inflation and Stock Returns
Over the long run investors enjoyed real rates ofreturn on common stock. However, over shorter
periods, inflation can and did exceed the nominal
rates thus producing negative rates of return anddisappointed investors who regarded equities as ahedge against inflation.
As the investment horizon is increased, returns
on common stocks outpaced inf lation over more
per iods and to a greater degree than the other
assets and were more volati le than any of them.
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Effects of Inflation
Assume the historical inflation rate =
3.1%.The value of one Dirham in:
417.0)0301.01(130
5526.0)0301.01(120
74337.0)0301.01(110
30
20
10
AEDAEDyears
AEDAEDyears
AEDAEDyears
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Effects of Inflation
Inflation can relegate
even the mostconservative
investments in tospeculative status.