FINS1613 Lecture Notes - Lecture 6: Systematic Risk, Risk Premium, Expected Return

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16 May 2018

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Chapter 12: Systematic Risk and the Equity Risk Premium

How to measure systematic risk to compute expected return

- portfolio: collection of securities- securities in portfolio + amount invested in each

security

- return of a portfolio is a weighted avg of returns on indiv securities (% of total value)

o RP= A*RA + B*RB +… *R

o R(%) and A + B +…  = 1

- Volatility of a portfolio- total risk measured as SD

o Combining shares into a portfolio reduces risk through diversification

o Amount of risk that is eliminated in a portfolio depends upon the degree to

which the shares face common risks and move together

▪ Correlation: measure of the degree to which returns share common

risk- covariance of the returns ÷ by product of SD of each return [-1:1]

- Risk benefit is the correlation coefficient p(ab) [-1:1]

- Without p- means no risk benefit from building portfolio

- Worst case: no benefit to building a portfolio p=1

- The expected return of a portfolio = weighted avg expected return of its shares, but

the volatility of a portfolio is less than the weighted avg volatility- ie eliminate some

volatility by diversifying

- There is a direct and proportional relationship between risk and return for large portfolios.

Returns increase in a consistent manner with the level of risk.

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Document Summary

Chapter 12: systematic risk and the equity risk premium. How to measure systematic risk to compute expected return. Risk benefit is the correlation coefficient p(ab) [-1:1] Without p- means no risk benefit from building portfolio. Worst case: no benefit to building a portfolio p=1. The expected return of a portfolio = weighted avg expected return of its shares, but the volatility of a portfolio is less than the weighted avg volatility- ie eliminate some volatility by diversifying. There is a direct and proportional relationship between risk and return for large portfolios. Returns increase in a consistent manner with the level of risk. Value weighted portfolio: portfolio in which each security is held in proportion to its market cap. Market proxy: a portfolio whose return is believed to closely track the true market portfolio. Market index: market value of a broad-based portfolio of securities. Return to systematic risk should always be the same.

Related Questions

1. The diversification effect of a portfolio of two stocks: . A. increases as the correlation between the stocks declines. B. increases as the correlation between the stocks rises. C. decreases as the correlation between the stocks rises. D. Both A and C. E. None of the above. 2. Irene Adler is considering investing in the common stock of Holmes and Watson. The following data are available for the two securities. . ................... Expected Return ..... Standard Deviation Holmes .............. 0.12 ......................... 0.08 Watson ............. 0.19 .......................... 0.25 . If she invests 60% of her funds Holmes and 40% in Watson, and if the correlation of returns between these two securities is 0.45, what is the portfolioâs expected return and standard deviation? . A. 14.8% and 12.89% B. 13.6% and 11.03% C. 14.6% and 13.94% D. 14.4% and 11.03% E. 13.21% and 10.08% 3. What does a security bring to the risk of a well diversified portfolio? . A. It brings its standard deviation of possible returns. B. It brings its covariance with the other securities in the portfolio. C. It brings its total risk. D. It brings its unsystematic risk. 4. Diversification can effectively reduce risk. Once a portfolio is diversified, the type of risk remaining is: . A. individual security risk. B. riskless security risk. C. unsystematic risk D. systematic risk 5. Efficient portfolios are those, which offer: . A. Highest expected return for a given level of risk B. Highest risk for a given level of expected return C. The maximum risk and expected return D. All of the above

Hi guys could someone help me and explain in detail the two fundamental principles of investments â the risk/return tradeoff and diversification. Also, describe how asset allocation and the correlation of various securities within asset classes impact the riskiness of an investorâs portfolio.

I found an answer but it seems to me very long and not sure about it so can you help me out guys

ANS:

Risk /Return Tradeoff

Risk, return and liquidity are three dimensions of investment decision. Risk/Return trade off considers two dimension ie risk and return. As risk of an investment increases , its expected return will decrease. Risk is measured by volatility of return which can be statistically obtained by standard deviation of return. Higher the standard deviation, higher will be volatility of return and higher the risk

Risk can be also measured as a relative risk compared to the market. This is measured by stock beta with reference to a market index. Higher the beta, higher the value of stock Beta, higher will be the risk .

Investors seeking higher return will need to take higher risks.

Treasury bonds are almost risk free assets. This has the lowest rate of return. Stocks have higher risk , hence have higher expected return. High beta stocks will have higher risk and higher returns.

An investor should understand his risk taking ability and will have to make a trade off between risk and return depending on his risk apetite.

Diversification:

There is a saying, do not put all your eggs in one basket. The reason is that it has higher risk if all eggs are in one basket. If the eggs are distributed in different basket, risk of loss decreases.

Same principle is applied in investment. Diversification reduces risk.

If one invests in different classes of assets like bonds, stock, commodities and properties âhis risk is likely to reduce. Reduction in return in one asset is likely to be compensated by return in other asset.

Within one class of asset also, there should be diversification to reduce risk.

For example one stock âA âmay have expected return of 10% and standard deviation of 5%.This risk can be reduced by diversification in number of assets and the ratio of Risk/return can be decreased.

If we diversify and instead of investing 100% in stock A, we invest 60% in âAâ and 40% in another stock âBâ having expected return15% and standard deviation of 8%.assume the correlation between the two assets are 0.5

Portfolio return=wa*Ra+wb*Rb

Wa=Weight of asset A=0.6

Wb=Weight of asset B=0.4

Ra=Return of A=10%

Rb=Return of B=15%

Sa=Standard deviation of A=5%

Sb=Standard deviation of B=8%

Corr(a,b)=Correlation of A & B=0.2

Portfolio return=0.6*10+0.4*15=12%

Portfolio Variance=(wa^2)*(Sa^2)+(wb^2)*(Sb^2)+2wa*wb*Cov(a,b)

Cov(a,b)=Corr(a,b)*Sa*Sb=0.1*5*8=4

Portfolio Variance=(0.6^2)*(5^2)+(0.4^2)*(8^2)+2*0.6*0.8*4=23.08

Portfolio standard deviation=Square root of Variance=(23.08^0.5)=4.8%

The diversification has increased return and reduced risk

Stock A was giving 10% return with 5% standard deviation. With diversification of portfolio we have 12% return and 4.8% standard deviation. Risk return ratio is decreased.

It may be noted that, higher the correlation between assets in the portfolio, higher will be risk in terms of standard deviation. Hence it is better to diversify with uncorrelated assets.

Diversification reduces unsystematic risk,but it cannot reduce systematic risk of overall market or economy

QUESTION 17

Unsystematic risk:

	A.	can be effectively eliminated through portfolio diversification.
	B.	is compensated for by the risk premium.
	C.	is measured by beta.
	D.	cannot be avoided if you wish to participate in the financial markets.
	E.	All of the above.

3 points

QUESTION 18

The diversification effect of a portfolio of two stocks:

	A.	increases as the correlation between the stocks declines.
	B.	increases as the correlation between the stocks rises.
	C.	decreases as the correlation between the stocks rises.
	D.	Both A and C.
	E.	None of the above.

3 points

QUESTION 19

Irene Adler is considering investing in the common stock of Holmes and Watson. The following data are available for the two securities.

................... Expected Return ..... Standard Deviation

Holmes .............. 0.12 ......................... 0.08

Watson ............. 0.19 .......................... 0.25

If she invests 60% of her funds Holmes and 40% in Watson, and if the correlation of returns between these two securities is 0.45, what is the portfolioâs expected return and standard deviation?

	A.	14.8% and 12.89%
	B.	13.6% and 11.03%
	C.	14.6% and 13.94%
	D.	14.4% and 11.03%
	E.	13.21% and 10.08%

FINS1613 Lecture Notes - Lecture 6: Systematic Risk, Risk Premium, Expected Return

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