Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) =...
-
Upload
sandra-holt -
Category
Documents
-
view
215 -
download
0
Transcript of Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) =...
![Page 1: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/1.jpg)
Risk and ReturnPrimer
![Page 2: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/2.jpg)
Expectations
Expected value (μ) is weighted sum of possible outcomes
E(X) = μ = p1X1 + p2X2 + …. psXs E(X) – Expected value of XXi – Outcome of X in state ipi – Probability of state is – Number of possible statesProbabilities have to sum to 1
p1 + p2 + …..+ ps = 1
2
![Page 3: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/3.jpg)
3
Horse Race
There are three horse racing in the Finance Derby. Your horse is “Love of NPV”. If your horse has a 30% chance of coming in first, and a 40% chance of coming in second. How much do you expect your horse to win? 1st pays $1,500 2nd pays $750 3rd pays $250
![Page 4: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/4.jpg)
4
Horse Race
There are three horse racing in the Finance Derby. Your horse is “Love of NPV”. If your horse has a 30% chance of coming in first, and a 40% chance of coming in second. How much do you expect your horse to win? 1st pays $1,500, 2nd pays $750, 3rd pays $250
Chance of coming in 3rd: 1-0.3-0.4 = 0.3 0.3*1,500 + 0.4*750 + 0.3*250 = $825
![Page 5: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/5.jpg)
5
What is risk?
Uncertainty
![Page 6: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/6.jpg)
6
Measuring Risk There is no universally agreed-upon
measureHowever, variance and standard deviation are both
widely accepted measures of total risk
![Page 7: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/7.jpg)
7
Statistics Review: Variance Variance (σ2) measures the dispersion of
possible outcomes around μ Standard deviation (σ) is the square root of
variance Higher variance (std dev), implies a higher
dispersion of possible outcomesMore uncertainty
![Page 8: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/8.jpg)
8
Different Variances
![Page 9: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/9.jpg)
9
Variance Calculation Variance = σ2 = Σpi * (Xi – μ)2: Use this one
Alternative formulas you may have seen σ2 = Σ(Xi – μ)2 / N σ2 = Σ(Xi – μ)2 / (N-1)
All give similar answers with large samplesBUT each give very different answers with small
samples
Ex. s=3σ2 = p1 * (X1 – μ)2 + p2 * (X2 – μ)2 + p3 * (X3 – μ)2
![Page 10: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/10.jpg)
10
Risk Example
Economy is “Good” with 20% probability DJIA will return 20%
Economy is “Fair” with 30% probability DJIA will return 5%
Economy is “Bad” with 50% probability DJIA will return -9%
![Page 11: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/11.jpg)
11
Calculations
Expected Return =
Variance =
Standard Deviation =
![Page 12: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/12.jpg)
12
Calculations
Expected Return = p1X1 + p2X2 + p3X3 = 0.2*0.20+0.3*0.05+0.5*(-0.09) = 0.01
Variance =
Standard Deviation =
![Page 13: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/13.jpg)
13
Calculations
Expected Return = 0.01
Variance = p1(X1- μX)2+p2(X2-μX)2+p3(X3-μX)2
=0.2*(0.20-0.01)2 + 0.3*(0.05-0.01)2 + 0.5*(-0.09-0.01)2
= 0.0127 =127 (%)2
Standard Deviation =
![Page 14: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/14.jpg)
14
Calculations
Expected Return = 0.01
Variance = 0.0127 =127 (%)2
Standard Deviation = √ σ2 √0.0127 = 0.113 = 11.3%
![Page 15: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/15.jpg)
15
Historical Data
In practice we do not know all of the possible states of the world, so we use historical data to form expectationsIdea: Look at what has happened in the past and
we can calculate the mean and variance What is each states probability of occurring?
![Page 16: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/16.jpg)
16
Risk Example 2
Sample Mean = 0.2*0.20+0.2*0.15+0.2*(-0.05)+0.2*0.05+0.2*0.10 = 0.09 = 9%
Sample Variance = = 0.2*(0.20-0.09)2 + 0.2*(0.15-0.09)2 + 0.2*(-0.05-0.09)2 + 0.2*(0.05-0.09)2 + 0.2*(0.10-0.09)2 = 74%2
Standard Deviation = √0.0074 = 0.086 = 8.6%
1996 1997 1998 1999 2000
20% 15% -5% 5% 10%
![Page 17: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/17.jpg)
17
Risk
A risky asset is one in which the rate of return is uncertain.
Risk is measured by ________________
![Page 18: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/18.jpg)
18
Risk
A risky asset is one in which the rate of return in uncertain.
Risk is measured by standard deviation. higher σ → more uncertainty
![Page 19: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/19.jpg)
19
General Securities
T-bills are a very safe investment No default risk, short maturity Risk free asset
Stocks are much riskier Bond’s riskiness is between T-bills and Stocks
![Page 20: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/20.jpg)
Why Do We Demand a Higher Return Investors seem to dislike risk (ex. insurance)
Risk Averse If the expected return on T-Bills (risk-free), is
10%, and the expected return for Ford is 10%, which would you buy?The 10% offered by T-Bills is guaranteed while
this is not the case for FordA guaranteed 10% dominates a possible 10%
20
![Page 21: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/21.jpg)
21
Return Breakdown
A risky asset’s return has two components:Risk free rate + Risk premium
Risk free rate: The return one can earn from investing in T-Bills
Risk Premium: The return over and above the risk free rateCompensation for bearing risk
![Page 22: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/22.jpg)
Average Risk Premiums (1926-2005)
Small company stocks : 17.4% – 3.8% = 13.6%
Large company stocks : 12.3% – 3.8% = 8.5%
Long-term corporate bonds : 6.2% – 3.8% = 2.4%
The more risk the larger the risk premium
22
![Page 23: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/23.jpg)
23
The Risk-Return Tradeoff
2%
4%
6%
8%
10%
12%
14%
16%
18%
0% 5% 10% 15% 20% 25% 30% 35%
Annual Return Standard Deviation
Ann
ual R
etur
n A
vera
ge
T-Bonds
T-Bills
Large-Company Stocks
Small-Company Stocks
Highest Risk & Return: Small Cap Stocks, Large Cap Stocks, L.T. Corp bonds, L.T. Gov Bonds, U.S. T-Bills
![Page 24: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/24.jpg)
24
Quick Quiz
Which of the investments discussed has had the highest average return and risk premium?
Which of the investments discussed has had the highest standard deviation?
![Page 25: Risk and Return Primer. Expectations Expected value (μ) is weighted sum of possible outcomes E(X) = μ = p 1 X 1 + p 2 X 2 + …. p s X s E(X) – Expected.](https://reader035.fdocuments.in/reader035/viewer/2022062806/5697bfd11a28abf838caaef9/html5/thumbnails/25.jpg)
Why we care?
This is the very basics of investing General knowledge that “finance” people
possess
25