FIN 302 Lecture Notes - Lecture 19: Weighted Arithmetic Mean, S&P 500 Index, Capital Structure

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15 Apr 2017

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Session 19: beta as a measure of systematic risk. Investors can eliminate non-systematic risk by holding a diversified portfolio (an exchange-traded fund that follows a market index) Since non-systematic risk can be eliminated nearly costlessly, investors are not compensated for bearing this risk. Systematic risk cannot be diversified away by holding more stocks, and investors require compensation for their exposure to this risk. Beta - a measure of security"s sensitivity to market risk. A and m - standard deviation of returns for security a and the market portfolio, respectively. Pa,m - correlation between returns of security a and the market. The asset returns are negatively correlated with the stock market. Gold during recessions (i. e. rn bc foreign policy) Asset returns are uncorrelated with the stock market. Asset is positively correlated with the market, but has lower exposure to systematic risk. Asset has the same exposure to systematic risk as the market portfolio.

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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

6. Institutional portfolios can take advantage of what is called "portfolio margining" under the rules of the CBOE and other options exchanges. What IS portfolio margining? Choose only one answer.

A. You only pay attention to the bottom margin of the portfolio.

B. Great leverage is possible, as the intercorrelations and natural offsets (or what we call in English a "wash") are taken into consideration.

C. No margin is required, because these are not individual investors.

7. What does the symbol ^VVIX mean?

A. Apple's volatility.

B. An exchange-traded (ETF) volatility fund.

C. The implied volatility of the VIX options themselves.

8. An example of purchasing a "real" option is a company's opening of a Shanghai office, in order to have the capacity to pursue business in China.

True

False

9. A hedge fund is "short" a portfolio of VIX call options. It's "theta" is $16,788 per day. This means, barring some big market or political or terrorist event, the fund's net asset value will increase by about $16,788 per day.

True

False

10. Imagine an equity-oriented state pension fund (such as the State of Maryland Pension funds). Suppose their equity portfolio is NOT identical to the S&P 500 index. Further, suppose that due to a state budget shortfall, the year's additions to the pension fund are likely to be less than actuarially sound. Thus, the fund is becoming very risk-averse. And it needs to implement this feeling by hedging. CHOOSE THE BEST ANSWER, even though there might be more than one true answer. This is actually a question about hedge ratios. A. If the equity portfolio's beta is close to 0, then they could decide to match the overall exposure, via S&P Index futures contracts, to the fund's value. That is, # of contracts times the contract multiplier times the index would approximately equal the value of the fund.

B. If the equity portfolio's beta is close to .4, then they would have a tough time using S&P 500 contracts, so they would instead use foreign exchange contracts.

C. If the equity portfolio's beta is close to 1, then they could decide to match the overall exposure, via S&P Index futures contracts, to the fund's value. That is, # of contracts times the contract multiplier times the index would approximately equal the value of the fund.

11. Go to CMEGROUP.COM We are going to hedge ULSD https://en.wikipedia.org/wiki/Ultra-low-sulfur_diesel for a railroad, that uses ultra-light diesel fuel. Choose June 2017 as the underlying future. Let's pretend we are buying ten futures contracts. What would ten contracts cost you, using the last trade as our price? Show your math, i.e., #gallons times price per futures contract. Is this contract in contango, or normal backwardation?

12. Long options positions(long does not mean long-dated) have positive gamma, and short positions have negative gamma.

True

False

13. In valuing credit default swaps, one must estimate default probabilities. A start would be to obtain historical data for default rates from rating agencies such as Standard & Poor's. But a more complete risk profile, or risk prediction, limiting ourselves to the US market (US-based companies) would be to [pick only one choice, the best one, in your opinion]:

A. Also consider the risk of another earthquake in Japan.

B. Also consider the systematic risk associated with an economic downturn in the US, accompanied by a downturn in US stocks.

C. Also consider the possibility that Facebook options are trading at an implied volatility that is not as high as it should be, considering the lofty level of its P/E ratio.

14. A total return swap can be a form of financing vehicle to allow an investor to buy a specific bond, because: (there are two correct answers, you must pick two)

A. The payer (a financial institution) could agree to pay the bond's capital appreciation or depreciation, plus the interest payments, in return for receiving LIBOR plus some basis points.

B. The payer (a financial institution) could agree to receive the bond's capital appreciation or depreciation, plus the interest payments, in return for receiving LIBOR plus some basis points.

C. The payer retains ownership of the bond for the life of the contract.

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FIN 302 Lecture Notes - Lecture 19: Weighted Arithmetic Mean, S&P 500 Index, Capital Structure

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