Lecture 01
Investment Compiled by
Dr. Kumail Rizvi, CFA, FRM
• Kumail Rizvi
PhD from Paris 1 (Panthéon sorbonne) 2011
CFA 2010
FRM 2010
MSc Money Banking and Finance 2007
MSc Computer Sciences 2003
MBEcon (Finance) 2001
Experience (Academic)
GIFT University
Hailey College of Commerce, Punjab University
PAK AIMS
IBP (Institute of Bankers Pakistan)
Paris 1 (Panthéon Sorbonne)
University of Central Punjab (UCP)
Lahore School of Economics (LSE)
Experience (Corporate)
NATIXIS BANK, France
Sigma Financials, Dubai
Synergistic Financial Advisors (SFA)
SPM Consulting, Dubai
SAS Middle East
IBM (International Business Machines)
GBM (Gulf Business Machines)
Chapter 1
The Investment Setting Questions to be answered:
• Why do individuals invest ?
• What is an investment ?
• How do we measure the rate of return on
an investment ?
• How do investors measure risk related to
alternative investments ?
Chapter 1 The Investment Setting • What factors contribute to the rates of
return that investors require on
alternative investments ?
• What macroeconomic and
microeconomic factors contribute to
changes in the required rate of return for
investments ?
Why Do Individuals
Invest ?
By saving money (instead of
spending it), individuals tradeoff
present consumption for a larger
future consumption.
04.1$%400.1$
How Do We Measure The Rate Of
Return On An Investment ? The pure rate of interest is the
exchange rate between future
consumption (future dollars) and
present consumption (current
dollars). Market forces determine
this rate.
People’s willingness to pay the
difference for borrowing today and
their desire to receive a surplus on
their savings give rise to an interest
rate referred to as the pure time
value of money.
How Do We Measure The Rate Of
Return On An Investment ?
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.
How Do We Measure The Rate Of
Return On An Investment ?
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.
How Do We Measure The Rate Of
Return On An Investment ?
Defining an Investment
A current commitment of $ for a period of time in order to derive future payments that will compensate for:
– the time the funds are committed
– the expected rate of inflation
– uncertainty of future flow of funds.
Measures of Historical Rates of Return
Holding Period Return
10.1 $200
$220
Investment of Value Beginning
Investment of Value EndingHPR
1.1
Measures of Historical Rates of Return
Holding Period Yield
HPY = HPR - 1
1.10 - 1 = 0.10 = 10%
1.2
Annual Holding Period Return
–Annual HPR = HPR 1/n
where n = number of years investment is held
Annual Holding Period Yield
–Annual HPY = Annual HPR - 1
Measures of Historical Rates of Return
Measures of Historical Rates of Return
Arithmetic Mean
1.4
yields period holding
annual of sum the HPY
:where
HPY/AM
n
Measures of Historical Rates of Return
Geometric Mean
1.5
n
n
HPRHPRHPR
:follows as returns period holding annual theofproduct the
:where1HPR GM
21
1
Portfolio Return Measurement
• Money ($) Weighted Rate of Return
– IRR is indeed the money weighted rate of return
because it accounts for the timing and amount of all
dollar flows into and out of the portfolio.
• Time Weighted Rate of Return
– It measures the compound rate of growth of $1
initially invested in the portfolio over a stated
measurement period.
– It is not affected by cash withdrawals or additions to
the portfolio.
Time Outlay
0 $200 to purchase the first share
1 $225 to purchase the second share
Proceeds
1 $5 dividend received from first share (not reinvested)
2 $10 dividend received from two shares
2 $470 received from selling two shares @$235 each
Money Weighted ROR
• PV(outflows) = PV (inflows)
• IRR Function: CF0=-200, CF1=-220,
CF2=480 IRR=9.39%
• Simple Arithmetic Mean of HPY or HPR
• (5+225)/200=1.15 or 15%
• (10+470)/450= 1.06777 or 6.67%
• Average: (15+6.67)/2 =10.84%
Time Weighted ROR
• It is indeed a Geometric Mean of HPRs or
1+HPYs
• TW-ROR = (1.15 x 1.0667)1/2 -1=10.76%
A Portfolio of Investments
The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPYs for the individual investments in the portfolio, or the overall change in the value of the original portfolio
Computation of Holding
Period Yield for a Portfolio # Begin Beginning Ending Ending Market Wtd.
Stock Shares Price Mkt. Value Price Mkt. Value HPR HPY Wt. HPY
A 100,000 10$ 1,000,000$ 12$ 1,200,000$ 1.20 20% 0.05 0.010
B 200,000 20$ 4,000,000$ 21$ 4,200,000$ 1.05 5% 0.20 0.010
C 500,000 30$ 15,000,000$ 33$ 16,500,000$ 1.10 10% 0.75 0.075
Total 20,000,000$ 21,900,000$ 0.095
21,900,000$
20,000,000$
HPY = 1.095 - 1 = 0.095
= 9.5%
HPR = = 1.095
Exhibit 1.1
Expected Rates of Return
• Risk is uncertainty that an
investment will earn its expected
rate of return
• Probability is the likelihood of an
outcome
Expected Rates of Return
n
i 1
i
Return) (Possible Return) ofy Probabilit(
)E(R Return Expected
)R(P....))(R(P))(R[(P nn2211
))(RP(1
ii
n
i
1.6
Risk Aversion
The assumption that most investors
will choose the least risky
alternative, all else being equal and
that they will not accept additional
risk unless they are compensated in
the form of higher return
Probability Distributions
Risk-free Investment
0.00
0.20
0.40
0.60
0.80
1.00
-5% 0% 5% 10% 15%
Exhibit 1.2
Probability Distributions
Risky Investment with 3 Possible Returns
0.00
0.20
0.40
0.60
0.80
1.00
-30% -10% 10% 30%
Exhibit 1.3
Probability Distributions
Risky investment with ten possible rates of return
0.00
0.20
0.40
0.60
0.80
1.00
-40% -20% 0% 20% 40%
Exhibit 1.4
Measuring the Risk of Expected Rates of Return
2n
1i
Return) Expected-Return (Possibley)Probabilit(
)( Variance
2
iii
1
)]E(R)[RP(
n
i
1.7
Measuring the Risk of Expected Rates of Return
Standard Deviation is the square
root of the variance
1.8
Measuring the Risk of Expected Rates of Return
Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return
Standard Deviation of Returns Expected Rate of Returns
E(R)
i
1.9
Measuring the Risk of Historical Rates of Return
variance of the series
holding period yield during period I
expected value of the HPY that is equal
to the arithmetic mean of the series
the number of observations
2/nn
1i
i
2 HPY)(EHPY[
n
E(HPY)
HPY
i
2
1.10
Determinants of Required Rates of Return
• Time value of money during the
period of investment
• Expected rate of inflation during
the period
• Risk involved
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
Adjusting For Inflation
Real RFR =
1Inflation) of Rate(1
RFR) Nominal1(
1.12
Nominal Risk-Free Rate
Dependent upon
– Conditions in the Capital Markets
– Expected Rate of Inflation
Adjusting For Inflation
Nominal RFR = (1+Real RFR) x (1+Expected Rate of Inflation) - 1
1.11
Facets of Fundamental
Risk
• Business risk
• Financial risk
• Liquidity risk
• Exchange rate risk
• Country risk
Business Risk
• Uncertainty of income flows caused by
the nature of a firm’s business
• Sales volatility and operating leverage
determine the level of business risk.
Financial Risk
• Uncertainty caused by the use of debt financing.
• Borrowing requires fixed payments which must be paid ahead of payments to stockholders.
• The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium.
Liquidity Risk
• Uncertainty is introduced by the secondary
market for an investment.
– How long will it take to convert an investment
into cash?
– How certain is the price that will be received?
Exchange Rate Risk
• Uncertainty of return is introduced by
acquiring securities denominated in a
currency different from that of the investor.
• Changes in exchange rates affect the
investors return when converting an
investment back into the “home” currency.
Country Risk
• Political risk is the uncertainty of returns
caused by the possibility of a major change
in the political or economic environment in
a country.
• Individuals who invest in countries that
have unstable political-economic systems
must include a country risk-premium when
determining their required rate of return
Risk Premium
f (Business Risk, Financial Risk,
Liquidity Risk, Exchange Rate
Risk, Country Risk)
or
f (Systematic Market Risk)
Risk Premium
and Portfolio Theory
• The relevant risk measure for an individual asset is its co-movement with the market portfolio
• Systematic risk relates the variance of the investment to the variance of the market
• Beta measures this systematic risk of an asset
Fundamental Risk
versus Systematic Risk • Fundamental risk comprises business risk,
financial risk, liquidity risk, exchange rate
risk, and country risk
• Systematic risk refers to the portion of an
individual asset’s total variance attributable
to the variability of the total market portfolio
Relationship Between Risk and Return Exhibit 1.7
Rateof Return
Risk(business risk, etc., or systematic risk-beta)
RFR
SecurityMarket Line
LowRisk
AverageRisk
HighRisk
The slope indicates therequired return per unit of risk
(Expected)
Changes in the Required Rate of Return Due to Movements Along the SML
Rate
Risk(business risk, etc., or systematic risk-beta)
RFR
SecurityMarket Line
Expected
Movements along the curvethat reflect changes in therisk of the asset
Exhibit 1.8
Changes in the Slope of the SML
RPi = E(Ri) - NRFR
where:
RPi = risk premium for asset i
E(Ri) = the expected return for asset i
NRFR = the nominal return on a risk-free asset
1.13
Market Portfolio Risk
The market risk premium for the market
portfolio (contains all the risky assets in the
market) can be computed:
RPm = E(Rm)- NRFR where:
RPm = risk premium on the market portfolio
E(Rm) = expected return on the market portfolio
NRFR = expected return on a risk-free asset
1.14
Change in Market Risk Premium
Exhibit 1.10
Risk
RFR
Original SML
New SML
Rm
Rm'
E(R)
NRFR
Expected Return
Rm´
Rm
Capital Market Conditions, Expected Inflation, and the SML
Exhibit 1.11
Risk
RFR
Original SML
New SML
Rate of Return
RFR'
NRFR
NRFR´
Expected Return
The Internet Investments Online
http://www.finpipe.com
http://www.investorguide.com
http://www.aaii.com
http://www.economist.com
http://www.online.wsj.com
http://www.forbes.com
http://www.barrons.com
http://fisher.osu.edu/fin/journal/jofsites.htm
http://www.ft.com
http://www.fortune.com
http://www.smartmoney.com
http://www.worth.com
http://www.money.cnn.com
Future Topics
Chapter 2
• The asset allocation decision
• The individual investor life
cycle
• Risk tolerance
• Portfolio management