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Consider the following case:

Andre is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in his portfolio are shown in the following table:

What is the expected return of Andre's stock portfolio?

a) 15.53%

b) 10.35%

c) 7.76%

d) 13.97

Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p=0.4) with each of the other stocks.  If the weighted average of the risk (standard deviation) of the individual securities in the partially diversified portfolio of four stocks is 40%, the portfolio's standard deviation () most likely is _______ 40 %.

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Ronaldo Mendoza
Ronaldo MendozaLv10
23 Jan 2021

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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 portfolio’s 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 – 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 investor’s 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 –his 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 “A “may 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 “A” and 40% in another stock “B” 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

Evaluating risk and return

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 40% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.
CVx =
CVy =

Which stock is riskier for a diversified investor?

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.

For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X.


-Select-IIIIIIIVVItem 3

Calculate each stock's required rate of return. Round your answers to two decimal places.
rx = %
ry = %

On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor?
-Select-Stock XStock YItem 6

Calculate the required return of a portfolio that has $4,500 invested in Stock X and $9,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.
rp = %

If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?
-Select-Stock XStock Y

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