fio unit 3
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Unit 3The Risk and
Rewards ofInvestment
Joey LaiITP-Vietnam Banking Academy,
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Content
the concept of return, its components,
the forces that affect the investors level of
return,
the role of time value of money inmeasuring return
Calculation of return, simple interest and
compound interestDescribe real, risk-free, and required returns
;
the key sources of risk that might affect
potential investment vehicles.
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Risk and Reward Theory
The risk-reward theory is the concept
that there should be a proportional
relationship between the amount ofrisk an investment contains and the
potential reward the investment
offers.
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Risk and Return Trade-Off
The relationship between risk and
return, in which investments with morerisk should provide higher returns, andvice versa.
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Figure 3.1: Risk Tolerance
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Individual Attitudes to Risk
Research shows that attitudes to investmentrisk depend on factors such as personality,
circumstances, level of financial knowledge
and experience, and extent of financialproduct holding.
Quantitative research carried out in the US
identified a similar range of factors, includingincome, wealth, age, marital status, gender
and level of education.
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Risk Profiler
Very cautious
cautious
Moderately cautious
Balanced
Moderately adventurous
Adventurous
Very adventurous
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Example:
I just want to make a quick profit
Its more important to me topreserve what I have than to make
big gains in the markets
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Definition
Return
Total Return:the sum of theincome and the capital gain (or
loss) earned on an investment overa specified period of time
The level of profit from aninvestment, or the reward forinvesting
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Sources of Investment Returns
Investments provide two basic types of return:
Income returns
The owner of an investment has the right to any cash flows
paid by the investment. Changes in price or value
The owner of an investment receives the benefit of
increases in value and bears the risk for any decreases in
value.
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Income Returns
Cash payments,usually receivedregularly over the life
of the investment.
Examples: Couponinterest paymentsfrom bonds, Commonand preferred stockdividend payments.
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Returns From Changes in Value
Investors also experience
capital gains or losses as
the value of their
investment changes overtime.
For example, a stock may
pay a 1 dividend while its
value falls from 30 to 25over the same time
period.
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Rate of return required to cover investment risk
and the anticipated decline due to inflation, in the
general purchasing power of the cash that the
investment generates
Nominal Rate of Return vs. RealRate of Return
The annual percentage return realized on aninvestment, which is adjusted for changes in
prices due to inflation or other external effects.
Nominal Rate of Return
Real Rate of Return
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Annualized Returns
If we have return or income/price change
information over a time period in excess of one year,
we usually want to annualize the rate of return in
order to facilitate comparisons with otherinvestment returns.
Another useful measure:
Return Relative = Income + Ending Value
Purchase Price
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Time Value of Money
A dollar received today is worth more than a dollar
received in the future
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Simple Interest vs. Compound Interest
Interest is paid only on
the initial deposit
Interest is paid on the
initial deposit and any
interest accumulated
from prior periods Interest is earned on
interest
More frequent
compounding periods
provide higher true rate
of interest
Compounding periods
range from annually to
continuously
Simple Interest Compound Interest
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SI = P0(i)(n)
Simple Interest Formula
Formula
SI: Simple Interest
P0: Deposit today (t=0)i: Interest Rate per Period
n: Number of Time Periods
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SI = P0(i)(n)
= $1,000(.07)(2)
= $140
Simple Interest Example
Assume that you deposit $1,000 in an account
earning 7% simple interest for 2 years. What
is the accumulated interest at the end of the2nd year?
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The Present Value is simply the
$1,000you originally deposited.
That is the value today!
Present Value is the current value of a futureamount of money, or a series of payments,
evaluated at a given interest rate.
Simple Interest (PV)
What is the Present Value (PV) of the previous
problem?
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FV1 = P0(1+i)1 = $1,000(1.07)
= $1,070
Compound Interest
You earned $70 interest on your $1,000
deposit over the first year.
This is the same amount of interest you wouldearn under simple interest.
Future Value
Single Deposit (Formula)
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FV1 = P0(1+i)1
FV2 = P0(1+i)2
General Future Value Formula:
FVn = P0(1+i)n
or FVn= P0(FVIFi,n) -- See Table I
General Future Value
Formula
etc.
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Julie Miller wants to know how large her deposit of$10,000today will become at a compound annual interest
rate of 10%for 5 years.
Story Problem Example
0 1 2 3 4 5
$10,000
FV5
10%
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Calculation based on Table I:
FV5 = $10,000(FVIF10%, 5)= $10,000(1.611)
= $16,110 [Due to Rounding]
Story Problem Solution
Calculation based on general formula: FVn = P0(1+i)
n
FV5 = $10,000(1+0.10)5= $16,105.10
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Assume that you need $1,000in 2 years. Letsexamine the process to determine how much youneed to deposit today at a discount rate of 7%
compounded annually.
0 1 2
$1,000
7%
PV1PV0
Present Value
Single Deposit (Graphic)
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PV0= FV2/ (1+i)2 = $1,000/ (1.07)2 = FV2
/ (1+i)2 = $873.44
Present Value
Single Deposit (Formula)
0 1 2
$1,000
7%
PV0
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Julie Miller wants to know how large of a deposit
to make so that the money will grow to $10,000 in
5 yearsat a discount rate of 10%.
Story Problem Example
0 1 2 3 4 5
$10,000
PV0
10%
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Calculation based on general formula:
PV0 = FVn/ (1+i)n
PV0 = $10,000 / (1+0.10)5
= $6,209.21
Calculation based on Table I:
PV0 = $10,000 (PVIF10%, 5)= $10,000(.621) =
$6,210.00 [Due to Rounding]
Story Problem Solution
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General Formula:
FVn = PV0(1 + [i/m])mn
n: Number of Yearsm: Compounding Periods per Yeari:
Annual Interest Rate FVn,m:
FV at the end of Year nPV0: PV of the Cash Flow today
Frequency of
Compounding
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What is risk?
Risk is the uncertainty associated with the return on
an investment.
Risk can impact all components of return through:
Fluctuations in income returns; Fluctuations in price changes of the investment;
Fluctuations in reinvestment rates of return.
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Figure 3.3 Risk Tolerance
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Acceptable Levels of Risk Depend Upon the
Individual Investor
Risk-indifferent describes an investor who does not requirea change in return as compensation for greater risk
Risk-averse describes an investor who requires greaterreturn in exchange for greater risk
Risk-seeking describes an investor who will accept a lowerreturn in exchange for greater risk
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Figure 3.2 Risk-Return Tradeoffs
for Various Investment Vehicles
K
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Steps in the Decision Process:
Combining Return and Risk
Estimate the expected return using present value methodsand historical/projected return rates
Assess the risk of the investment by looking at
historical/projected returns using standard deviation orcoefficient of variation of returns
Evaluate the risk-return of each investment alternative tomake sure the return is reasonable given the level of risk
Select the investment vehicles that offer the highestexpected returns associated with the level of risk you arewilling to accept
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Measures of Risk: Single Asset
Standard deviation is a statistic usedto measure the dispersion (variation)
of returns around an assets average
or expected return
s2= SPi(Ri-E(R))2
Coefficient of variation is a statistic used to measure the
relative dispersion of an assets returns; it is useful in
comparing the risk of assets with differing average orexpected returns.
CV = s/RA
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THANKS!
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