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Finance  Ch 13
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Terms in this set (57)
expected retun
The return on an asset expected in the future
Expected Return
Expected Return = (Probability that the state occurs)(Rate if State Occurs) + (Probability that state2 occurs)(Rate if State2 Occurs)
Risk Premium
Projected Risk Premium = Expected Return  Riskless Rate
How to calculate the variance
1. Determine the squared deviations from the expected return (Difference between the actual rate and the expected return. Then square it)
2. Multiply
each
STD by its probability
3. Add these up (That will give you the variance)
(To get STD, find the square root of the variance)
Variance Equation
Variance = p1(r1Er)^2+p2(r2Er)
p1= probability that state 1 occurs
r1=actual rate in state 1
Er= Expected Return (same for all states)
When given the Expected Return and the STD, you can
find the interval of rates possible.
Expected Return = 25%
Standard Deviation = 45%
That means...
You could potentially get as much as 70% from this investment (25%+45%). And you could get as little as 20% (lose 20%) from this invest (25%45%=20%)
Portfolio
A group of assets such as stocks and bonds held by an investor
Portfolio weight
The percentage of a portfolio's total value that is invested in a particular asset
= Value of Particular Asset / Total Value of Portfolio
Weights are in
DECIMAL
form
Portolio Return
The return you receive when a state occurs (i.e. if the economy goes into a recession)
Rp= (Weight1)(Rate1)+(Weight2)(Rate2)
= (.50)(.2)+(.50)(.3%)
= .05 = 5%
Weight1 = Portfolio weight for asset number 1. (Asset Value/Total Portfolio Value)
Rate 1 = Individual Expected Return for Asset 1
Basically for each.... Weight*Individual Expected Return
Then add them all up
The riskreturn tradeoff for a portfolio is measured by the ....
portfolio expected return and standard deviation
p. 427 example. tricky
How to find Portfolio Variance
Find expected return for each state (weight)((Actual))
Find expected return for portfolio as a whole (probability)((Average))
Find portfolio variance and standard deviation
1. Compute portfolio return for
EACH
of the n states
rpA = W1R1 + W2R2
W1= Weight of Asset 1
R1 = Rate if state occurs
W2 = Weight of Asset 2
R2 = Rate if state occurs
2. Compute expected
portfolio
return
ER = P1(rpA) + P2(rpB) + P3(rpC)
P1 = Probability that state 1 occurs
rpA = expected return for state A
3. Compute portfolio variance and standard deviation
same equation as before
Expected Returns versus Unexpected Returns

Realized returns
are generally not equal to
expected
returns (bc of unexpected returns)
 At any point in time, the unexpected return can be either positive or negative
 Over time though, the average of the unexpected component is 0
Total Return on a stock = Expected Return + Unexpected Return
= E(R) + U
= E(R) + Systematic Risk + Unsystematic Risk
Unexpected Returns (EXAMPLES)
 News about company research
 Future news about the company (good or bad)
 Announcement of higher sales than expected
 Sudden drop in interest rates
Announcements and News
 announcements and news contain
both
an expected component and a surprise component (I knew sales were going to increase, but I didn't think they would go up by that much. WOW!)
 The surprise component affects the stock price and therefore its return
The risk of any investment comes from the
unanticipated events. Risk comes from the surprises.
If there were no surprises, everyone would get exactly what they expected and investments would riskfree
Systematic risk
 one type of surprise or unexpected return
 risk that influences
a lot of assets
 correlated price changes
 also called "market risk" or "nondiversifiable risk"
ex. General economic conditions (GDP, interest rates, inflation), inflation, taxes, war
Unsystematic risk
 risk that only affects at most a small number of assets

UN
correlated price changes
 also called unique or assetspecific risks or idiosyncratic risk
ex. the announcement of an oil strike by a company (will affect that company and few others like their competitors and suppliers)
 part shortages, discoveries, luck
Portfolio Diversification
the investment in several different asset classes or sectors that don't move together
 Diversification is
not
just holding a lot of assets
ex. If you own 50 internet stocks, you are not diversified

diversifying your portfolio eliminates risk!!!!
Principle of Diversivation
 Diversification can substantially reduce the
variability
of returns without an equivalent reduction in expected returns
 risk is reduces because expected returns can be good for one asset and bad for another, therefore offset
 However, there is a minimum level of risk that
cannot
be diversified away (systemic portion)
Diversifiable Risk
 risk that
can be
eliminated by combining assets into a portfolio
 often considered the same as Unsystemic risk
 If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk we could diversify away
Why is portfolio diversification important?
Because the STD of annual portfolio returns decreases as you increase the number of stocks in your portfolio
Standard deviation of Annual portfolio returns decline as
the number of stocks in Portfolio increases
How does diversification reduce unsystematic risk?
The reduction in risk happens because
worse
than expected returns by one asset, can be
offset
by
better
than expected returns from another asset due to
uncorrelated
events (which is why diversification only works when you have assets that react differently to the market)
There is a minimum level of risk that ________
There is a minimum level of risk that CANNOT be diversified away (systematic risk)
What kind of risk cannot be diversified away?
Systematic Risk
Diversifiable risk
 Risk that can be eliminated by combining assets into a portfolio
 aka unsystematic risk
 Holding assets in the same industry exposes ourselves to risk that
we could diversify away
Examples of ways to diversify
Dow Jones 
30 stocks that are major factors in their industries
NASDAQ 
4000 companies, domestic and international
S&P 500 
500 largest companies in the US.
As # of stocks in your portfolio increases, unsystematic risk will
DECREASE
As # of stocks in your portfolio increases, proportion of systematic risk will
INCREASE. closer and closer to 1
Because unsystematic risk is risk that you can avoid, you want to get rid of as much as you can. So,
that there is only systematic risk, or risk that is unavoidable or out of your control. Interest rates, irregular or unusual events
The standard deviation of returns is a measure of
total risk
Total Risk =
Total Risk = Systematic risk + Unsystematic risk
The Total Risk for a diversified portfolio is essentially just the
systematic risk
Systematic Risk Principle
 there is a reward for bearing risk
 there is NOT a reward for bearing risk
unnecessarily

expected return on a risky asset depends only on that asset's systematic risk
(since unsystematic risk can be diversified away)
How do we measure Systematic Risk?
Beta coefficient
Smaller the beta, the smaller the expected return
Because: the less systematic risk in the asset, the less likelihood to earn higher rewards
Beta and Risk Premium
Higher the beta, higher the risk premium
(Systematic Risk principle)
Total Risk versus Beta
Security A
STD: 40%
Beta: 0.5
Security B
STD: 20%
Beta: 1.50
Greater total risk?
A. Higher STD
Greater systematic risk?
B. Higher Beta
Greater unsystematic risk?
A. Lower Beta
Which asset will have higher risk premium?
B. Because the Systematic risk principle. Only rewarded for risk that is systematic. Because the STD is high in A but has a lot of unsystematic risk, the expected return will be lower than B
How to calculate Portfolio Beta?
Multiply the
weight
of each asset by the beta coefficient of each asset. Add them up
How to calculate expected return of the Portfolio?
Multiply weight by expected return of each asset. Add them up
Beta results:
Beta = 1 Asset has same systematic risk as the overall market
Beta < 1 Asset has
less
systematic risk than the overall market
Beta > 1 Asset has
more
systematic risk than the overall market
Beta = 0 Asset has no systematic risk (TBill)
(overall market is also called
average asset
)
Why are some beta values just question marks?
? means no beta coefficient because the company is
not
publicly traded
What is the beta of a
risk free
asset
0
Why?
Because by definition, a risk free asset has no systematic risk
As Portfolio Beta increases, Portfolio Expected Return _______
Also increases
As Portfolio Beta increases, Portfolio Expected Return also increases
RewardtoRisk Ratio
Same for all assets and portfolios
(E(R)R(f))/B
(Expected Return  Risk Free Rate)/Beta
OR
Risk Premium/Beta
20%8%/1.6 = 7.5%
Asset A has a risk premium of 7.5 percent per "unit" of systematic risk
Use this ratio when comparing Assets with E(R) and B
Risk Free rate is always 8%
All assets and portfolios must have the same RewardtoRisk Ratio because
if they have different Ratio's then the prices and returns will be adjusted to equilibrium by market purchasing and selling of assets
Market Equilibrium
RewardtoRisk Ratio's are equal for all assets
 NPV of 0
Market Disequilibrium (asset too high)
Asset RewardtoRisk Ratio > Market RewardtoRisk Ratio
 above the SML line
 Postive NPV (market value>cost)
 price is too low (worth more than it costs)
 We buy the asset, price of asset goes up, Expected return goes down, ratio goes down (back to equilibrium)
Market Disequilibrium (asset too low)
Asset RewardtoRisk Ratio < Market RewardtoRisk Ratio
 below the SML line
 Negative NPV (market value<cost)
 Price is too high
 We want to sell the asset, price of asset falls, expected return goes up, ratio goes up (back to equilibrium)
Security Market line Graph:
X axis: Asset Beta
Y axis: Asset Expected Return
Slope: Rewardtorisk ratio
Interpretation: All assets must have the same Rewardtorisk ratio, aka must have the same slope, so they must be on the line
How can points be off the line?
Different Rewardtorisk ratios
How?
When comparing two assets with different Beta and Expected return, Asset A has a risk ratio of 6.15% and Asset B has a risk ratio of 5%.
Conclusion: B's price is too high. REWARDtorisk ratio, the reward is too small compared to risk, or expected return is too small relative to the risk. So, the price is too high and is overvalued. And we would see its price fall.
Security Market Line (SML)
Graph of beta and expected returns
Describes relationship between systematic risk and expected return
SML slope
SML slope is E(Rm)  Rf
Expected Return on the market portfolio  Riskfree asset rate
(Beta is 1 because its the markets portfolio)
 SML slope is also called the
market risk premium
because it is the risk premium on a market portfolio
Prior to this chapter, Mark has given us the expected return. But now we can. So, how can we find an assets expected return?
CAPM
Capital Asset Pricing Model
Capital Asset Pricing Model (CAPM)
 defines the relationship between risk and return
Expected Return = Risk Free Rate + (Beta of Asset)(Expected Market Risk Premium)
If we know an asset's systemic risk, we an use the CAPM to find its expected return
Factors that affect Expected Return
 Pure time value of money = reward for waiting for your money. Measured by the Risk Free Rate
 Reward for bearing systematic risk = measured by the market risk premium
 Amount of systematic risk = measured by Beta
Example of CAPM
Beta = 1.74
Riskfree rate = 4%
Market Risk Premium = 8%
What is the expected return?
CAPM = 4 + 1.74(8) = 17.92%
What is the average market return?
12%
= 4 + 1(8)
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