FINE 2000 Lecture Notes - Lecture 1: Expected Return, Risk-Free Interest Rate, Systematic Risk

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cerisehorse97

15 Sep 2016

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Market index: a measure of the investment performance of the overall market: looking at the average risk on the market today (stocks) Treasury bill is a promise from the government (bond) The stock is a hope therefore you could face a loss. Psychologically, the loss is more than the gain leads to the idea of risk aversion. A higher risk should lead to a higher return/reward: rate of return on any security = rate of return on tbill + rate of return on . A way to look at it, how predictable is the outcome. T-bills have the lowest average rate of return and the lowest level of volatility. Stocks have the highest average rate of return and the highest level of volatility. 0. 3 x 122. 22 + 0. 5 x 13. 33 + 0. 2 x (-100) = 23. 33% Normal: 1 + (26 25)/25 = 0. 08.

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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

1. In the statement, "Based on the period 1950 â 1999, you would have the less uncertainty about any expected return on small company stocks than you would about the expected return on 3-month T-Bills.", changing "3-month T-Bills" to "large company stocks" would result in the statement being True.

2. In the statement, "Our author discusses the average return and standard deviation for 3 different assets for the period 1950 â 1999.", changing "3" to "4" would result in the statement being True.

3.In the statement," âDiversifiableâ risk, âCompany-specificâ risk, âSystematicâ risk and âMarketâ risk all refer to the same type of risk.", changing "Systematic" to "Unsystematic" would result in the statement being True.

4.In the statement, "By diversifying you can eliminate most or all of Systematic risk.", changing "Systematic" to "Unsystematic" would result in the statement being True. In the statement, "The variance is the square root of the standard deviation.", switching "variance" and "standard deviation" would result in the statement being True.

5.In the statement, "A stock with one-half the average market risk would have a value for beta of 2.0.", changing "2.0" to "0.5" would result in the statement being True.

6.In the statement, "The only variable on the right-hand side of the CAPM formula that varies from one company to another is the risk-free rate.", changing "risk-free rate" to "expected return on the market" would result in the statement being True.

7.In the statement, "In order to properly evaluate a stock, investors need only consider its risk premium.", changing "risk premium" to "risk" would result in the statement being True. In the statement, "Investors should always choose stocks with the lowest reward-risk ratio.", changing "lowest" to "highest" would result in the statement being True.

8.In the statement, "To find the standard deviation, we take the square root of the sum of the deviations of each observation from the mean of the observations.", changing "deviations" to "squared deviations" would make the statement True.

9. In the statement, "When working with the entire population of observations, the denominator of the variance calculation is (n -1).", changing "(n - 1)" to "n" would result in the statement being True. In the statement, "Ceteris paribus, higher standard deviations represent lower risk.", changing "higher" to "lower" would result in the statement being True.

scarlettermite470

I need help proof reading my assignment please, thank you in advance.

Cost of Debt

The cost of debt is the effective rate that a company pays on its total debt.

As a company acquires debt through various bonds, loans and other forms of debt, the cost of debt is a useful metric. It gives an idea as to the overall rate being paid by the company to use debt financing. This measure is also useful because it gives investors an idea as to the riskiness of the company compared with others. The higher the cost of debt, the higher the risk.

1. Cost of debt (before tax) = Corporate Bond rate of companyâs bond rating.

Pepsico 2.75% = 2.75%

Current cost of Debt as of February 17th 2014 = 2.75%

2. Current tax rate

In 2013 PepsiCoâs tax rate was = 23.66%

2013 PepsiCo averaged tax rate of 23.66%

3. Cost of Debt (After Tax) = (Cost of Debt Before Tax) (1 â Tax Rate)

The effective rate that a company pays on its current debt after tax.

.0275 x (1 â .2366) = Cost of debt after tax

The cost of debt after tax for PepsiCo is 2.10%

Cost of Equity or R Equity = Risk Free Rate + Beta Equity (Average Market Return â Risk Free Rate)

The cost of equity is the return a firm theoretically pays to its equity investors to compensate for the risk they undertake by investing in their company.

Risk Free Rate = U.S. 10-year bond = 2.74%

Average Market Return 1950 â 2014 = 7%

Beta = PepsiCoâs Beta = 0.37

Risk Free Rate + Beta Equity (Average Market Return â Risk Free Rate)

2.74 + 0.37 (7- 2.74)

2.74 + 0.37 x 4.26

2.74 + 1.58 = 4.31%

Currently, PepsiCoâs has a Cost of Equity or R Equity of 4.31%, so investors should expect to get a return of 4.31% per-year average over the long term on their investment to compensate for the risk they undertake by investing in this company.

Weighted Average Cost of Capital or WACC calculation

The WACC calculation is a calculation of a companyâs cost of capital in which each category of capital is equally weighted. All capital sources such as common stock, preferred stock, bonds and all other long-term debt are included in this calculation.

As the WACC of a firm increases, and the beta and rate of return on equity increases, this is an indicator of a decrease in valuation and a higher risk. By taking the weighted average, we can see how much interest the company has to pay for every dollar it finances. For this calculation, you will need to know the following listed below:

Tax Rate = 23.66%

Cost of Debt (before tax) or R debt = 2.75%

Cost of Equity or R equity = 4.31%

Debt (Total Liabilities) for 2013 TTM or D = $53.069 billion

Stock Price = $78.09 (Feb. 17th, 2014)

Outstanding Shares = 1.55 billion

Equity = Stock price x Outstanding Shares or E = $121.04 billion

Debt + Equity or D+E = $174.109 billion

WACC = R = (1 â Tax Rate) x R debt (D/D+E) + R equity (E/D+E)

(1 â Tax Rate) x R debt (D/D+E) + R equity (E/D+E)

(1 â .2366) x .0275 x ($53.069 /$174.109) + .0431 ($121.04 /$174.109)

.7634x .0275 x .3048 + .0431 x .6972

.0064 + .03

= 3.64%

Based on the calculations above, we can conclude that PepsiCo pays 3.64% on every dollar that it finances, or 3.64% cents on every dollar. From this calculation, we understand that on every dollar the company spends on an investment, the company must make $.0673 plus the cost of the investment for the investment to be feasible for the company.

Understanding the WACC of a company is important because securities analysts employ WACC all the time when valuing and selecting investments. In discounted cash flow analysis, for instance, WACC is used as the discount rate applied to future cash flows for deriving a businessâs net present value.

Investors use WACC as a tool to decide whether to invest. The WACC represents the minimum rate of return at which a company produces value for its investors. Letâs say a company produces a return of 20% and has a WACC of 11%. That means that for every dollar the company invests into capital, the company is creating nine cents of value. By contrast, if the companyâs return is less than WACC, the company is shedding value, which indicates that investors should put their money elsewhere.

FINE 2000 Lecture Notes - Lecture 1: Expected Return, Risk-Free Interest Rate, Systematic Risk

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