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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!