# Risk and Return

```Risk and Return Intro
Returns
 HPR
 CAGR
 YTM, RCYTM
 APR and APY
 DY
 NPV, IRR
 Average Annual Return
 Geometric Return
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Holding Period Return (HPR)
 Holding Period Return
 The total return earned from holding an investment for a
specified holding period (usually 1 year or less)
Holding period return 
Current income
Capital gain (or loss)

during period
during period
Beginning investment value
Capital gain (or loss)
Ending
Beginning


during period
investment value
investment value
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Using HPR
 Advantages of Holding Period Return
 Easy to calculate
 Easy to understand
 Considers current income and growth
 Disadvantages of Holding Period Return
 Does not consider time value of money
 Inaccurate and irrelevant if time period if longer than one
year
3
Using IRR
 Advantages of Internal Rate of Return
 Uses the time value of money
 Allows investments of different investment periods to be
compared with each other
 If the yield is equal to or greater than the required return, the
investment is acceptable
 Disadvantages of Internal Rate of Return
 Calculation is complex
 Results may not be unique
4
Interest on Interest
 Using YTM and IRR assumes:
that all income earned over the investment
horizon is reinvested at the same rate as the
original investment.
 Reinvestment Rate is the rate of return earned on
interest or other income received from an investment
over its investment horizon.
 Fully compounded rate of return is the rate of return
that includes interest earned on interest.
5
Risk
between risk and
 Pr(relationship
r) r
return, in which investments with more risk should provide
higher returns, and vice versa
 Return, for purposes of planning, is the expected return.
E( R)   Pr(r ) r
 Risk is the chance that the actual return from an investment
may differ from what is expected. Measured as the
standard deviation of the expected return.
6
Risk and
Prices
andexpected
Coupon Return
Rates
E(r)
Risk
r
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Sources of Risk
uncertainty associated with an investment’s earnings
and ability to pay returns owed investors.
 Affects
 Common stocks
 Preferred stocks
 Examples
 Decline in company profits or market share
8
Sources of Risk (cont’d)
 Currency Exchange Risk
variation in exchange rates.
 Affects
 International bonds
 Examples
 U.S. dollar appreciates against foreign currency, reducing
value of foreign investment
9
Sources of Risk (cont’d)
 Financial Risk
uncertainty attributable to the mix of debt and equity
more debt, greater this risk.
 Affects
 Common stocks
 Corporate bonds
 Examples
 Company unable to obtain credit to fund operations
 Company defaults on bonds
10
Sources of Risk (cont’d)
changing price levels (inflation or deflation) that
 Affects
 Bonds (fixed income)
 Certificates of deposit
 Examples
 Barrel of oil \$66.00 last year is \$89.00 this year
11
Sources of Risk (cont’d)
 Interest Rate Risk
changes in interest rates that adversely affect a
security’s value.
 Affects
 Bonds (fixed income)
 Preferred stocks
 Examples
 Market values of existing bonds decrease as market interest
rates increase
 Income from an investment is reinvested at a lower interest
rate than the original rate
12
Sources of Risk (cont’d)
 Liquidity Risk
not being able to liquidate an investment conveniently
and at a reasonable price.
 Affects
 Some small company stocks
 Real estate
 Examples
 Selling a low volume stock reduces the price of the stock,
consider blockage discounts
13
Sources of Risk (cont’d)
 Tax Risk
Congress may introduce unfavorable tax laws, driving
down the after-tax returns and market values of
certain investments.
 Affects
 Municipal bonds
 Real estate
 Examples
 Lower tax rates reduce the tax benefit of municipal bond
interest
 Limits on deductions from real estate losses
14
Sources of Risk (cont’d)
 Market Risk
decline in investment returns because of market factors
independent of the given investment.
 Affects
 All types of investments
 Examples
 Stock market decline on bad news
 Political upheaval
 Changes in economic conditions
15
Sources of Risk (cont’d)
 Event Risk
unexpected events that have significant and immediate
effect on the underlying value of an investment.
 Affects
 All types of investments
 Examples
 Decrease in value of insurance company stock after
a major hurricane
 Decrease in value of real estate after a
major earthquake
 The BP oil spill
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Measures of Risk: Single Asset
 Standard deviation is a statistic
used to measure the

CV 

dispersion (variation) of returns
around an asset’s
average or expected return.
 Coefficient of variation is a statistic used to measure
the relative dispersion of an asset’s returns; it is useful
in comparing the risk of assets with differing average or
expected returns.

CV 

 Higher values for both indicate higher risk
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Historical Returns and Risk
18
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The Decision Process:
Combining Return and Risk

Estimate the expected return using present value methods and
historical/projected return rates.

Assess the risk of the investment by looking at
historical/projected returns using standard deviation or
coefficient of variation of returns.

Evaluate the risk-return of each investment alternative to make
sure the return is reasonable given the level of risk.

Select the investment vehicles that offer the highest expected
returns associated with the level of risk you are willing to accept.
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```
Investment

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Lehman Brothers

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