Risk and Return

Risk and Return              

 ““To win, you have to risk loss."”

-- Jean-Claude Killy, Olympic Skiing Champion "

In market there is always exist a trade-off between risk and return for securities, i.e. the higher the risk of a security, the higher the expected return will be.

 In Risk and Return, we will cover basic concepts

1)        Defining Risk and Return 

2)        Using Probability Distribution to Measure Risk 

a)         Probability Distribution          b)       Expected Return

c)         Standard Deviation                d)       Coefficient of Variation

3)        Attitudes toward Risk                               

4)        Risk and Return in a Portfolio Context

5)        The Capital Asset Pricing Model

6)        Diversification

7)        Efficient Financial Markets          

Diversification

Diversification                     

Diversification begins with a very beautiful quote.

“Don’t put all your eggs in one basket”.

The idea behind this is to diversify risk across a number of assets or investments.

So the main benefit of diversification is in the form of risk reduction.

To better grip the diversification, we must have knowledge of risks associated with investments.

So broadly, there are two types of risks.

·       Systematic Risk

·       Unsystematic Risk

Systematic Risk

It is the variability of return on portfolios associated with changes in return on the market as a whole.

Systematic Risk is due to risk factors that affect the overall market such as changes in the nation’s economy, changes in the world energy situation or a change in government policy. These are the risks that cannot be diversified away.

Unsystematic Risk

It is the variability of return on portfolios not explained by general market movements. It is avoidable through diversification.

Unsystematic risk is unique to a particular company or industry so it is independent of economic, political, and other factors that affect investments.

Unsystematic risk accounts for around 50 percent of the stock’s total risk.

So Total Risk = Systematic risk + Unsystematic risk

Risk and Return in a Portfolio Context

Risk and Return in a Portfolio Context            

Portfolio

It is combination of two or more securities or assets

Portfolio Return

The expected return of a portfolio is a weighted average of the expected returns of the securities constituting the portfolio.

For Example,

We have two securities, i.e. Security A and Security B and we have also their corresponding expected returns and standard deviation

                                       

	Security A	Security B
Expected Return	10%	12%
Standard Deviation	8%	5%

If equal amounts of money are invested in the two securities, the expected return of the portfolio is

(0.5)10% + (0.5)12% = 11%

Portfolio Risk

From the previous example our portfolio risk will be:

(0.5)8% + (0.5)5% = 5.25%

Portfolio risk is not so simple. To understand portfolio risk we must understand covariance

Covariance

It is a statistical measure of the degree to which two variables move together.

There are three different kinds of covariance directions.

Positive Covariance

It implies that the two variables move in the same direction.

Negative Covariance

It implies that the two variables move in the opposite direction.

Zero Covariance

It implies that the two variables show no tendency to vary together in either a positive or negative direction.

Conclusion

The riskiness of a portfolio depends much more on the paired security covariance than on the riskiness of the separate security covariance.

High covariance lead to high portfolio risk and

Low covariance lead to low portfolio risk

Attitude towards Risk

Attitude towards Risk            

Different kind of people has different kind of attitude towards risk.

We must keep in mind “risky investments must offer higher expected return, i.e. risk premium, than less risky investments in order for people to buy and hold them”

Risk Averse

This term is applied to an investor who demands a higher expected return, the higher the risk.

Risk indifference

This term is applied to an investor who demands an equal expected return, the equal the risk.

Risk preference

This term is applied to an investor who demands a more higher expected return, the more higher the risk.

Using Probability Distribution to Measure Risk

Using Probability Distribution to Measure Risk                             

Probability Distribution: It is a set of possible values that a random variable can assume and their associated probabilities of occurrence. For risky securities, the actual rate of return can be viewed as a random variable subject to a probability distribution. The probability distribution can be described in terms of two parameters. 1)    The expected return 2)    The standard deviation E xpected Return It is the weighted average of possible returns, with the weights being the probabilities of occurrence. So the expected return, R is: R = t=1∑ n(Ri)(Pi) Where Ri = the return for the ith possibility Pi = the probability of the return occurring N= the total number of possibilities S tandard Deviation It is a statistical measure of the variability of a distribution around its mean and it is the square root of the variance. We must keep in mind that, “The greater the standard deviation of returns, the greater the variability of returns and greater the risk of the investment”. The standard deviation can be expressed mathematically as σ = √ [t=1∑n( Ri - R‾)(Pi)] Where, Ri = Possible Return R‾= Expected Return Pi = Probability of Return occurring C oefficient of Variation It is the ratio of the standard deviation of a distribution to the mean of that distribution and it is the measure of relevant risk, i.e. a measure of risk per unit of expected return. Coefficient of Variation (CV) = σ/R‾ Where, σ = Standard deviation R‾= Expected Return “The larger the CV, the larger the relative risk of the investment”.

Defining Risk and Return

Defining Risk and Return                          

Risk

It is the variability of returns from those that are expected. It means your actual return on an investment may differ substantially from your expected return.

Treasury Bills would be a risk-free security whereas the common stock would be a risky security.

Because Treasury Bills are Government owned and the Government pays these bills. But common stock depends on company to company so there is a risk in that. So the conclusion is,

“The greater the variability, the risker the security is said to be,”

Return

It is the income received on an investment plus any change in the market price divided by the beginning price.

For Example,

You buy for $100 a security that would pay $10 in cash to you and be worth $110 one year later. The Return would be

($10 + $10)/$100 = 20%