This document provides an overview of key concepts in investment analysis and portfolio management. It discusses what constitutes an investment, factors that influence required rates of return such as time value of money, inflation, and risk. It also covers measures of historical and expected rates of return, risk of expected returns using variance and standard deviation, and the three determinants of required rates of return - the real risk-free rate, expected inflation, and risk premium.

1. Course: Investment Analysis
and Portfolio Management
(614)
Presented By
Sunanda Sarker
Roll NO. 161201
Batch-16
MBM, BIBM
Presented To
Dr. Prashanta Kumar
Banerjee
Professor & Director
(Research, Development

2. CHAPTER 1
The Investment Setting
•What Is An Investment
•Return and Risk Measures
•Measuring Historical Rates of Return
•Computing Mean Historical Return
•Calculating Expected Rates of Return
•Measuring the Risk of Expected Rates of
Return
•Determinants of Required Returns

3. What is an Investment?
Investment is the current commitment
of money for a period of time in order
to derive future payments that will
compensate for:
• Time the funds are committed
• Expected rate of inflation
• Uncertainty of future flow of funds

4. Why Invest?
• By investing (saving money now
instead of spending it), individuals
can tradeoff present consumption
for a larger future consumption.

5. Pure Time Value of Money
• People willing to pay more for the money
borrowed and lenders desire to receive a
surplus on their savings (money invested)

6. The Effects of Inflation
• Inflation
‒ If the future payment will be diminished in value
because of inflation, then the investor will
demand an interest rate higher than the pure
time value of money to also cover the expected
inflation expense.

7. Uncertainty: Risk by any
Other Name
• Uncertainty
• If the future payment from the investment is not
certain, the investor will demand an interest rate
that exceeds the pure time value of money plus
the inflation rate to provide a risk premium to
cover the investment risk.

8. Required Rate of Return
on an Investment
• Minimum rate of return investors require on
an investment, including the pure rate of
interest and all other risk premiums to
compensate the investor for taking the
investment risk

9. Measures of
Historical Rates of Return
Holding Period Return:
Ending Value of Investment
HPR =
Beginning Value of Investment
Holding Period Yield:
HPY = HPR – 1

10. Historical Rates of Return:
What Did We Earn (Gain)?
Example I:
Your investment of $250 in Stock A is worth $350 in two
years while the investment of $100 in Stock B is worth
$120 in six months. What are the annual HPRs and the
HPYs on these two stocks?

11. Your Investments Rise in Value
Example I:
• Stock A
– Annual HPR=HPR1/n = ($350/$250)1/2 =1.1832
– Annual HPY=Annual HPR-1=1.1832-1=18.32%
• Stock B
– Annual HPR=HPR1/n = ($112/$100)1/0.5 =1.2544
– Annual HPY=Annual HPR-1=1.2544-1=25.44%

12. Historical Rates of Return:
What Did We Lose?
Example II:
Your investment of $350 in Stock A is worth $250 in two
years while the investment of $112 in Stock B is worth
$100 in six months. What are the annual HPRs and the
HPYs on these two stocks?

13. Your Investments Decline in Value
Example II:
• Stock A
– Annual HPR=HPR1/n = ($250/$350)1/2 =.84515
– Annual HPY=Annual HPR-1=.84514 - 1=-15.48%
• Stock B
– Annual HPR=HPR1/n = ($100/$112)1/0.5 =.79719
– Annual HPY=Annual HPR-1=.79719-1=-20.28%

14. Calculating Mean Historical Rates
of Return
• Arithmetic Mean Return (AM)
AM= Σ HPY / n
where Σ HPY=the sum of all the annual HPYs
n=number of years
• Geometric Mean Return (GM)
GM= [π HPY]
1/n
-1
where π HPR=the product of all the annual HPRs
n=number of years

15. Arithmetic vs. Geometric Averages
• When rates of return are the same for all
years, the AM and the GM will be equal.
• When rates of return are not the same for
all years, the AM will always be higher
than the GM.
• While the AM is best used as an “expected
value” for an individual year, while the GM
is the best measure of an asset’s longterm performance.

16. Comparing Arithmetic vs. Geometric
Averages: Example
Suppose you invested $100 three years ago and it is
worth $110.40 today. What are your arithmetic and
geometric average returns?

17. Arithmetic Average: An Example
Year
Beg. Value
Ending
Value
HPR
HPY
1
$100
$115
1.15
.15
2
115
138
1.20
.20
3
138
110.40
.80
-.20
AM= Σ HPY / n
AM=[(0.15)+(0.20)+(-0.20)] / 3 = 0.15/3=5%
GM= [π HPY] 1/n -1
GM=[(1.15) x (1.20) x (0.80)]1/3 – 1
=(1.104)1/3 -1=1.03353 -1 =3.353%

18. Portfolio Historical Rates of Return
• Portfolio HPY
‒ Mean historical rate of return for a portfolio of investments
is measured as the weighted average of the HPYs for the
individual investments in the portfolio, or the overall
change in the value of the original portfolio.
• The weights used in the computation are the
relative beginning market values for each
investment, which is often referred to as dollarweighted or value-weighted mean rate of return.

19. Expected Rates of Return
What Do We Expect to Earn?
• In previous examples, we discussed realized
historical rates of return.
• In reality most investors are more interested in the
expected return on a future risky investment.

20. Risk and Expected Return
• Risk refers to the uncertainty of the future
outcomes of an investment
• There are many possible returns/outcomes from
an investment due to the uncertainty
• Probability is the likelihood of an outcome
• The sum of the probabilities of all the possible
outcomes is equal to 1.0.

21. Calculating Expected Returns
n
E(R i ) = ∑ (Probability of Return) × (Possible Return)
i =1
= [(P1 )(R 1 ) + (P2 )(R 2 ) + .... + (Pn R n )]
n
= ∑( Pi )( Ri )
i=
1
Where:
Pi = the probability of return on asset i
Ri = the return on asset i

22. Perfect Certainty:
The Risk Free Asset
If you invest in an asset that has an expected return 5%
then it is absolutely certain your expected return will be
5%
• E(Ri) = ( 1) (.05) = .05 or 5%

23. Probability Distribution of Risk-free
Investment
Risk-Free Investment
1.00
0.80
0.60
0.40
0.20
0.00
-5%
0%
5% 10% 15%

24. Risky Investment with
Three Possible Outcomes
• Suppose you are considering an
investment with 3 different potential
outcomes as follows:
Economic
Conditions
Probability
Expected Return
Strong Economy
15%
20%
Weak Economy
15%
-20%
Stable Economy
70%
10%

25. Probability Distribution
Risky Investment with 3 Possible
Returns
1.00
0.80
0.60
0.40
0.20
0.00
-30%
-10%
10%
30%

26. Calculating Expected Return on a
Risky Asset
n
E ( Ri ) = ∑ ( Pi )( Ri )
i =1
1.00
0.80
0.60
0.40
0.20
0.00
-30%
-10%
10%
E ( Ri ) = [(.15)(.20) + (.15)(-.20) + (.70)(.10)] = .07 = 7%
Investment in a risky asset with a probability distribution as
described above, would have an expected return of 7%.
This is 2% higher than the risk free asset.
In other words, investors get paid to take risk!
30%

27. Risk and Expected Returns
• Risk refers to the uncertainty of an investment;
therefore the measure of risk should reflect the
degree of the uncertainty.
• Risk of expected return reflect the degree of
uncertainty that actual return will be different from
the expect return.
• Common measures of risk are based on the variance
of rates of return distribution of an investment

28. Risk of Expected Return
• The Variance Measure
Variance
n
Possible Expected 2
= ∑ (Pr obability ) x (
−
)
Re turn
Re turn
i =1
n
= ∑ Pi [ Ri − E ( Ri )]2
i =1

29. Risk of Expected Return
• Standard Deviation (σ)
• square root of the variance
• measures the total risk
σ=
n
− E ( Ri )]2
∑ Pi [ Ri
i =1
• Coefficient of Variation (CV)
• measures risk per unit of expected return
• relative measure of risk
Standard Deviation of Return
CV =
Expected Rate of Return
=σ
E (R)

30. Risk of Historical Returns
• Given a series of historical returns measured by
HPY, the risk of returns can be measured using
variance and standard deviation
• The formula is slightly different but the measure of
risk is essentially the same

31. Variance of Historical Returns
n

σ = ∑ [HPYi − E(HPY)]2  / n
 i =1

2
Where:
σ 2 = the variance of the series
HPY i = the holding period yield during period I
E(HPY) = the expected value of the HPY equal to the arithmetic
mean of the series (AM)
n = the number of observations

32. Three Determinants of
Required Rate of Return
• Time value of money during the time period
• Expected rate of inflation during the period
• Risk involved

33. Three Key Components of
Total Required Rate of Return

34. The Real Risk Free Rate (RRFR)
• Assumes no inflation
• Assumes no uncertainty about future cash flows
• Influenced by time preference for consumption of
income and investment opportunities in the
economy

35. Nominal Risk Free Rate (NRFR)
• Conditions in the capital market
• Expected rate of inflation
NRFR=(1+RRFR) x (1+ Rate of Inflation) - 1
RRFR=[(1+NRFR) / (1+ Rate of Inflation)] - 1

36. ?