1. Risk and Return

2. Defining Actual Return
Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment.
Dt + (Pt - Pt-1 )
R =
Pt-1

3. Defining Return: example
The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year?
$ ($ $10.00 )
= 0.05 = 5%
R =
$10.00

4. Defining Risk
Typically, investment returns are not known with certainty.
Investment risk pertains to the probability of earning a return less than that expected.
The greater the chance of a return far below the expected return, the greater the risk.
High levels of uncertainty (high risk) are associated with high potential returns. The risk/return tradeoff is the balance between the desire for the lowest possible risk and the highest possible return.

5. Risk Classification
It is possible to categorize the risks of the individual investments into two categories:
The systematic risk (or Market Risk) component measures the contribution of the investment to the risk of the market. For example: inflation, hike in corporate tax rate→ UNDIVERSIFIABLE RISK
The unsystematic risk is the element of risk that does not contribute to the risk of the market. This component is diversified away when the investment is combined with other investments. For example: Product recall, labor strike, change of management → DIVERSIFIABLE RISK

7. Measure of Risk: Variance
How do we measure risk?

8. Variance of a Stock
For example, consider the following two stocks, A and B, each of which has an expected return of 5 percent, as noted at the top of each table:
Both stocks have the same expected return. But even in the worst case, stock A still earns the investor 3 percent. On the other hand, stock B causes the investor to lose 5 percent in the worst case. This is a demonstration of why investors consider the variability of expected returns. Based on the individual's risk tolerance, a 3 percent return might be acceptable, but the risk of a 5 percent loss might be regarded as unacceptable.

9. Variance and Standard Deviation
Standard Deviation, σ, is a statistical measure of the variability of a distribution around its mean. It’s the square root of Variance, S2 (or, σ2).
The larger the standard deviation, the higher the probability that returns will be far below the expected return.
Two stocks may have the same expected return, but have different levels of risk.
Variance formula →

10. Calculating variance of a stock based on historical returns
Calculate the average historical return.
Calculate the difference between each observed return and the average return.
Square each difference.
Sum the squared differences.
Divide the sum of squared differences by the number of observations minus 1. The result of Step 5 is the sample variance.

11. How do we represent risk?
Normal Distribution
How do we represent risk?

12. Normal Distribution
As we have seen, any investment has two aspects: risk and return.
Investors look for the lowest possible risk for highest possible return.
The normal distribution quantifies these two aspects by the mean for return and standard deviation (or variance) for risk.

13. Normal Distribution: definition
The normal distribution is the probability distribution that plots all of its values in a symmetrical fashion.
The graph of the normal distribution depends on two factors - the mean and the standard deviation. The mean of the distribution determines the location of the center of the graph, and the standard deviation determines the height of the graph. When the standard deviation is large, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow.

14. Normal Distribution: example
Consider the following graphs for Conglomo, Inc. and Bilco, Inc. These graphs show the theoretical frequency distributions of the monthly returns for each firm's common stock as though the returns were normally distributed:
Conglomo's distribution of returns is more concentrated than Bilco's, as illustrated by Conglomo's relatively wider bell curve. A more concentrated distribution is defined as having a smaller standard deviation. The distribution curve appears higher, steeper, and narrower because more observations are occurring close to the expected return. Bilco's distribution is rather flat, reflecting that its returns are less concentrated, or more dispersed, than those of Conglomo Inc.

15. Normal Distribution (cont’d)
As we’ve seen before, standard deviation indicates the amount by which values deviate on average from the mean. The higher the standard deviation, the riskier the investment, as it leads to more uncertainty.
Hence, the graphical representation of normal distribution through its mean and standard deviation, enables representation of both returns and risk within a clearly defined range.
It helps to know (and be assured with certainty) that if some dataset follows the normal distribution pattern, its mean will enable us to know what returns to expect, and its standard deviation will enable us to know that around 68% of the values will be within 1 standard deviation, 95% within 2 standard deviations and 99% of values will fall within 3 standard deviations. A dataset which has mean of 1.5 and standard deviation of 1 is much riskier than another dataset having mean of 1.5 and standard deviation of 0.1.

16. Limitations
Mathematical models provide a good mechanism to quantify some variables with single, trackable numbers. Unfortunately, no mathematical model is perfect and each has inadequacies and limitations.
The basic assumption that stock price returns follow normal distribution itself is questioned time and again. There is sufficient empirical proof of instances where values fail to adhere to the assumed normal distribution.
Normal Distribution, which forms the basis of Portfolio Theory, may not necessarily apply to stocks and other financial asset price patterns.

17. How to the use Beta coefficient to measure systematic risk

18. Beta Coefficient
While standard deviation determines the volatility of a fund according to the disparity of its returns over a period of time, beta determines the volatility (or risk) of a fund in comparison to that of its index or benchmark.
Beta coefficient is a measure of sensitivity of a share price to movement in the market price
What does beta tell us?
A beta of 1 implies the asset has the same systematic risk as the overall market
A beta < 1 implies the asset has less systematic risk than the overall market
A beta > 1 implies the asset has more systematic risk than the overall market

19. How to calculate Beta
Beta = Covariance (between the asset and the market )/Variance of Market

20. Beta Coefficient: application
Investors can tailor a portfolio to their specific risk-return requirements, aiming to hold securities with betas in excess of 1 while the market is rising (because, if the market goes up, you’ll do better than the market), and securities with betas of less than 1 when the market is falling.
TICKER
COMPANY NAME
BETA
MKT CAP (Bil)
MKT CAP RANKING
NYSE:UAL
UNITED CONTINENTAL HOLDINGS INC.
0.67
$17.26
LARGE
NASDAQ:BOFI
BOFI HOLDINGS INC.
-0.04
$1.42
SMALL
NASDAQ:GOOG
ALPHABET INC.
0.93
$547.29
NASDAQ:AMZN
AMAZON.COM INC.
1.49
$393.96

21. Q&A