Understanding Risk. 1.What is risk? 2.How can we measure risk?
-
Upload
mariah-blankenship -
Category
Documents
-
view
219 -
download
0
Transcript of Understanding Risk. 1.What is risk? 2.How can we measure risk?
![Page 1: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/1.jpg)
Understanding Risk
![Page 2: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/2.jpg)
1. What is risk?
2. How can we measure risk?
![Page 3: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/3.jpg)
Risk and Investment Risk
• Risk in general : Chance that an unfavorable event will occur.
• Investment risk: the probability of earning less than expected.• The greater the chance of low or negative
returns, the riskier the investment
![Page 4: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/4.jpg)
Approach to Measuring Risk
• List of all possible outcomes
• List the chance of each one occurring
- Value between zero and 1
(probability)
![Page 5: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/5.jpg)
Measuring Risk - Simple Example Possibilities, Probabilities and Expected Value
List all possible outcomes and the chance of each one occurring
![Page 6: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/6.jpg)
Possibilities, Probabilities and Expected Value List all possible outcomes and the chance of each one occurring
• Toss 2 – Coins
• Is the outcome of the first coin dependent upon the outcome of the second coin?
• Invest in 2 stocks
Two Coin TossPossibilities Outcome Probability
#1
#2
#3
#4
![Page 7: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/7.jpg)
Measuring Risk: Example 1
$1000 Investment
Two Possibilities:1. Investment will rise in value to $1400
2. Investment will fall in value to $700
Suppose the two possibilities have equal chance of occurring -
- Probability of each outcome = 1/2
![Page 8: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/8.jpg)
Expected Value
Expected Value = ½ ($700) + ½ ($1400) = $1050
![Page 9: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/9.jpg)
Measuring Risk: Example 2 (more complicated)
$1000 Investment with four possibilities:
1. Rise in value to $2000
2. Rise in value to $1400
3. Fall in value to $700
4. Fall in value to $100
Chance (probability) of occurring =
0.1, 0.4, 0.4, 0.1
![Page 10: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/10.jpg)
Expected Value
Expected Value = 0.1x($100) + 0.4x($700) + 0.4x($1400) +0.1x($2000) = $1050
![Page 11: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/11.jpg)
Measuring Risk: Comparing Examples 1 and 2
• Example 1 and example 2 have the same expected value of $1050.
• The expected return is $50 on a $1000 investment, or 5%.
• However, the two investments have different levels of risk.
• The wider the distribution of payoffs, the higher the risk.
![Page 12: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/12.jpg)
Measuring Risk: Comparing Examples 1 & 2
Case 2 has a higher standard deviation because it has a bigger spread
![Page 13: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/13.jpg)
Measuring Risk• A risk-free asset is an investment whose future
value of known with certainty.
• This return is the referred to as a risk-free rate of return.
• If the risk-free return is 5 percent, a $1000 risk-free investment will pay $1050 - its expected value - with certainty.
• If there is a chance that the payoff will be either more or less than $1050, the investment is risky.
![Page 14: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/14.jpg)
Risk-Return Tradeoff
More risk Bigger risk premium Higher expected return
Risk Requires Compensation
![Page 15: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/15.jpg)
Measuring Risk - Standard Deviation
• Variance:
Average of squared deviation of the outcomes from the expected value, weighted by the probabilities.
• Standard Deviation:Square root of the variance(Same units as the payoff)
![Page 16: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/16.jpg)
Measuring Risk: Standard Deviation for Example 1
Step 1:Compute the expected value: ($1400 x ½) + ($700 x ½) = $1050.
Step 2: Subtract this from each of the possible payoffs:$1400-$1050= $350
$700-$1050= –$350
Step 3: Square each of the results: (+$350)2= 122,500 and (–$350)2= 122,500
![Page 17: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/17.jpg)
Measuring Risk: Standard Deviation for Example 1
Step 4: Multiply each result times its probability and add up the results:
½ [122,500] + ½ [122,500] = 122,500
So the calculation is:
Variance = ½($1400-$1050)2 + ½($700-$1050)2
= 122,500
![Page 18: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/18.jpg)
Measuring Risk: Standard Deviation for Example 1
• The standard deviation is the square root of the variance.
• Standard Deviation = $350
• Standard Deviation is more useful because in same units as payoff – dollars.
• Note: $350/$1000 = 35%
![Page 19: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/19.jpg)
Measuring Risk: Standard Deviation for Example 2
![Page 20: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/20.jpg)
Measuring Risk: Comparing Examples 1 & 2
Case 1: Standard Deviation =$350
Case 2: Standard Deviation =$528
The greater the standard deviation, the higher the risk.
![Page 21: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/21.jpg)
Value at Risk
• Sometimes we are less concerned with the spread of possible outcomes than we are with the value of the worst outcome.
• To assess this sort of risk we use a concept called “value at risk.” (VaR)
• VaR measures risk of the maximum potential loss.
• Formal definition: value at risk is the worst possible loss at a given probability.
![Page 22: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/22.jpg)
Value at Risk
• $300 loss in Example 1, 50% chance
• $900 loss in Example 2, 10% chance
• Lottery example: • Compare paying $1 for chance to win $1 million to
paying $10,000 for a chance to win $10 billion.
![Page 23: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/23.jpg)
Reducing Risk through Diversification
Spreading Risk
To spread your risk - find investments whose payoffs are completely unrelated.
![Page 24: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/24.jpg)
WHAT THE FINANCIAL SYSTEM DOESSharing Risk
• The financial system allows people to share risks:
• Savers can reduce risk through diversification: providing funds to many different investors with uncorrelated assets. • Banks do this by lending to different industries.
Also diversify geographically.• Mutual funds invest in common stock of many
different companies.
![Page 25: Understanding Risk. 1.What is risk? 2.How can we measure risk?](https://reader035.fdocuments.net/reader035/viewer/2022062423/56649e305503460f94b2171d/html5/thumbnails/25.jpg)
Reducing Risk through Diversification
• Diversification can reduce idiosyncratic risk (company specific risk), risks that differ across individual businesses.
• Diversification cannot reduce systematic risk (market risk), which affect most/all businesses
5-25