5016 - Investment and Financial Analysis - Personal Investment - Calculating Risk and Portfolio Theory p403 - 496 Flashcards
Risk is Volatility in Cashflows from…
- A Project (NPV based on forecast cashflow)
- Income (Interest/Dividends)
- Capital Gains (Sales - Purchases)
Volatility can be Measured by…
- Variance of periodic returns
- Standard Deviation of periodic returns
- Beta
What averages can be used to assess risk
Mean
Median
Mode
Variance
Are measures of how much the data varies or deviates from the mean
The mean of 4,5,6 is 5
The mean of 1,6,8 is 5
The second set of numbers has a greater variance
Standard Deviation
A quantity expressing how much the values differ or relate to the mean value of the entire group
How to calculate standard deviation
- Work out the mean
- From each number, subtract the mean and square the result
- Work out the mean of those squared differences
- Take the square root of that and that is it
Expected Value Standard Deviation Rule
If the return of project 1 is equal or more than project 2 and, the SD of project 1 is lower than project 2, project 1 should be done
or
If the expected return of project 1 is greater than project 2 and the SD of project 1 is equal to or more than project 2 it should be accepted
Risk depends upon what?
Covariance - how one performs and varies in comparison to the other
Correlation - The relation on investments in the portfolio e.g. if share A goes up and Share B goes down the Risk is offset
What determines the Risk of a 2 share portfolio
- Risk (SD) of asset/investment A by itself
- Risk (SD) of asset/investment B by itself
- Covariance/ Correlation between A and B
- Proportions of A and B in portfolio
What does Covariance show?
Positive Covariance shows a positive relationship between the returns of X and Y, negative shows the opposite. Looks at how one varies in relation to the other
What does Correlation show?
The correlation coefficient measures the strength of the relationship between A and B
What does r(Squared) represent
The Coefficient of Determination
What does the Coefficient of Determination indicate
It indicated the ‘explanatory power’ of the relationship, so by how much is an increase in costs explained by an increase in outputs (r^2)
What does the Coefficient of Determination Value show
The closer it is to 1, the greater its power, cannot rely on the relationship if it is not close to 1
For example if the change between the $ and Bitcoin was 0.85 or 85% we can see the change in the price of the dollar equates to 85% of the change in the price of Bitcoin, the other 15% would need to be investigated as this is down to other factors
What does The Correlation Coefficient Show
Indicates the strength of the relationship between 2 variables
The Correlation Coefficient has a value range of
-1 to 1
Correlation Coefficient Values and Meanings
r > 0 = They move in the same direction
r < 0 = They move in the opposite direction
r = 0 = No relationship
r = +1 = Perfectly Positive
r = -1 = Perfectly negative
Correlation Coefficient =
√r
Perfect Correlation
R = +1 is a perfectly positive correlation, goes up from left to right
R = -1 is a perfectly negative correlation goes down from left to right
For every unit increase or decrease in X, there is an equal increase or decrease in Y
Zero Correlation
r = 0, no correlation present
Partial Correlation
Where the data points are linked in a relationship.
Can either be positive or negative
Below 0.7 is considered a weak correlation and hence is unreliable
Calculating the Linear Regression Line (Correlation) y = bx + a
b =
nΣ XY – Σ X. Σ Y OVER nΣ X2 - (Σ X)2 (Gradient/slope)
a =
Σ Y - b Σ X OVER n (intercept of the line on the Y axis)
n = number of data pairs
Σ = Sum of total
Might need to know this for the exam, but id honestly rather die than try and figure this out on paper when we live in the 21st century - you would never need to do that in the real world
Fixed Costs
Costs that stay the same regardless of output
Variable Costs
Cost that change depending on output
What are Outliers?
An outlier is an observation that lies an abnormal distance from the other values in a random sample from a population, or an abnormal distance from the sample mean
Normal Distribution
Normal distribution is a probability distribution that is symmetric about the mean, showing the data near the mean are more frequent in occurrence than data far from the mean
Z Table in Normal Distribution
Also called a standard normal table, is a mathematical table showing the percentage of values below(to the left) a z score in normal distribution
Z Score
A Z score indicates how much a given value differs from the standard deviation
If market returns are normally distributed, then what are the values and deviation
95% of the values will lie +/- 2 Standard Deviation
Assessing Risk and Return Example using Standard Deviation
15% return with 3.5% risk, 7.2% 2 St Dev
15 +/- 7.2 = 7.8 - 22.2
How to calculate Z Value
(Return%+2StDev) - Return over Risk
The Determinants of NPV
- The Cashflow Forecast: Based on assumed sales volume and prices. Sell one unit less and the cashflow is different so NPV is too.
- The discount rate used which is derived from the estimated WACC
When hedging risk what should be undertook
Sensitivity Analysis and What-if scenario analysis
Considering Changes to WACC
Considered by:
- Adding a risk premium to WACC and discounting by a higher figure (10% not 8% say)
- Calculating the IRR to see how high the discount rate could go before 0 NPV
- CAPM or APT
Risk Adjusted Discount Rates Overview
- Risk adjusted discount rates will be better than WACC
- This would mean the company would require a different discount rate for every project based on:
- Project Data
- Cash flows
- Changes in return, risk free rates etc
The Capital Asset Pricing Model (CAPM) Summary
- CAPM is another way of calculating cost of capital.
Enables you to calculate the expected return for the risk you are taking. A risk adjusted measure of return
Capital Asset Pricing Model (CAPM) in short
Risk adjusted measure of return
Return you should receive for the risk you are taking
Minimum Return
The return you could get from investing Risk Free
Risk Premium
Compensation for risk, higher the risk, higher the compensation
Example of a Risk Free Investment
UK Government Bonds
Basic way to model return expected from risk being took
Risk Free option + Risk Premium or Compensation for risk
Compensation for Risk (Market Risk Premium) Example
If you earned 10% investing on the market when government bonds paid 4% risk free 10 - 4 = 6% Compensation for risk + 4% risk free
Compensation for Future Risk
Previous Compensation x Risk Factor (Periods), you can add this to expected risk free amount
What does CAPM mean in relation to risk?
CAPM = Rate you WANT for the risk your taking out
What does WACC mean in relation to risk?
WACC = The return you NEED to beat
What does NPV mean in relation to risk?
Need to be positive
What does IRR mean in relation to Risk?
The IRR value is the rate which would discount the project to 0
What is Beta
Beta is a measure of Market (Systematic, non-diversifiable) Risk
The volatility of the market as a whole is measured and given a Beta score of 1
The volatility of the market as a whole has a β = 1
A share with a β of 1 is
As sensitive to economic factors as the market as a whole
A share with a β of 1.4 is
Its roughly 40% more risky than the average in terms of market risk
A share with a β of 0.8
It roughly 20% less risky than the average in terms of market risk.
Beta - Market V Shares
Beta is a relative measure of market risk, showing the correlation between market and shares. It measures the sensitivity of an individual security relative to movements in the market
How to calculate / estimate Beta
Calculated by comparing the volatility of the market with the volatility of the share
cov(investment with market) OVER var(market)
Security Market Line (SML)
Line drawn on a chart that serves as a graphical representation of the capital asset ricing model (CAPM) which shows different levels of market risk of various securities against the expected return of the entire market at a given time
Problems of the CAPM Calculation
- Betas based on past trends
- Difficult to calculate non-listed companies
- The person teaching me it knows fuck all
Assumptions of CAPM
- Investors are rational and risk averse so prefer high returns and low risk
- Investors have similar expectations
- Single period time horizon. Time horizon means timeline but the lecturer is an insufferable prick and uses phrases without explaining
- Perfect Capital Markets - no taxes, no transaction costs and individuals can lend and borrow at the same time
CAPM and Discount Rate Problems
- CAPM is a single period return model, the discount rate required in an NPV calculation is multi period. Therefore CAPM discount rates are of limited use
- It is difficult to assess the beta for a project, may need to use industry average which is less accurate
CAPM Suggests…
Expected return on an asset depends on:
- Time value of money as measured by risk free rate of return
- Reward for bearing systematic risk as measured by the market risk premium
- Amount of systematic risk measured by Beta, relative to average asset
The Capital Asset Pricing Model: Theory and Evidence
Eugene F. Fama and Kenneth R. French. Journal of Economic
Perspective,Volume 18, Number 3,Summer 2004 - Findings Simplified
While returns do increase with beta the increase in returns is not
exactly as predicted by the CAPM theory. In general the relationship
has proved ‘flatter’ than predicted by the CAPM
Tests on CAPM findings in broad
- CAPM implies that differences in expected returns between assets and portfolios are entirely explained by differences in beta; other variables should add nothing to the explanation of expected return. This prediction plays a prominent role in tests of CAPM.
However, many studies suggest much variation in expected return is unrelated to beta
Studies into CAPM summarised findings
- Future returns on high earnings price ratio shares are higher than what CAPM predicts
- High debt-equity ratios are associated with returns that are too high relative to their market betas
- Shares with high book to market equity rations (B/M, the ratio of the book value of a share to its market value) have high average returns that are not explained by betas
- Ratios involving share prices have info about expected returns missed by market betas. A share price depends not only on expected cash flows it provides, but also on the expected returns that discount future expected cash flows
Arbitrage Pricing Theory Definition
APT is a multi-factor asset pricing model based on the idea an assets returns can be predicted using the linear relationship between the assets expected return and a number of macroeconomic variables. Alternative to CAPM
Alternative to CAPM
APT - Arbitrage Pricing Theory
What did Roll and Ross argue?
Argued that beta is too restrictive a measure of risk as several stocks may have the same beta but vastly different risk factors
Who developed APT
Ross (1976)
Roll and Ross (1980) four factor model of unanticipated changes
- Unanticipated changes in inflation
- Unanticipated changes in industrial production
- Unanticipated changes in yield between low and high grade bonds (default risk premium)
- Unanticipated changes in the yield differential between long and short terms bonds (term structure of interest rates)
CAPM Limitations
CAPM uses Beta (one factor) to capture risk which is only a relative measure of risk (relative to the market)
Roll and Ross argue beta is too restrictive a measure of risk as several stocks may have same beta but perform differently
