# Risk and Return

Topics: Capital asset pricing model, Modern portfolio theory, Normal distribution Pages: 9 (3586 words) Published: July 30, 2013
(1)Financial assets are expected to generate cash flows and hence the riskiness of a financial asset is measured in terms of the riskiness of its cash flows. (2)The riskiness of an asset may be measured on a stand-alone basis or in a portfolio context. An asset may be very risky if held by itself but may be much less risky when it is a part of a large portfolio. (3)In the context of a portfolio, the risk of an asset is divided into two parts: diversifiable risk (unsystematic risk) and market risk (systematic risk). Diversifiable risk arises from company-specific factors and hence can be washed away through diversification. Market risk stems from general market movements and hence cannot be diversified away. For a diversified investor what matters is the market risk and not the diversifiable risk. (4)In general, investors are risk-averse. So, they want to be compensated for bearing market risk. In a well-ordered market there is a linear relationship between market risk and expected return. (1) RISK AND RETURN OF A SINGLE ASSET: Capital gains/ loss yield Current Yield Rate of Return=[Annual income/Beginning price]+[{Ending price-Beginning price}/ Beginning price] OR Total return = Dividend + Capital gain=

Rate of return  Dividend yield  Capital gain yield R1  DIV1   P1  P  DIV1 P  P 0 0  1  P P P 0 0 0

(2) PROBABILITY DISTRIBUTION AND EXPECTED RATE OF RETURN: E(R)=∑(i=1 to n)=p(i) *R(i), where, E(R)=expected return, n=number of possible outcomes, p(i)=probability associated with R(i), R(i)=return for the ith possible outcome. (3)Standard Deviation of Return: Risk refers to the dispersion of a variable. It is commonly measured by the variance or the standard deviation. The variance of a probability distribution is the sum of the squares of the deviations of actual returns from the expected return, weighted by the associated probabilities.  2 = ∑ p(i)*{*R(i)-E(R)]} 2 where,  2 =variance, R®=return for the ith possible outcome, p(i)=probability associated with the ith possible outcome, E (R)=expected return. Since, variance is expressed as squared returns, it is somewhat difficult to grasp. So its square root, the standard deviation , is employed as an equivalent measure.  =( 2 ) ^(1/2), =standard deviation. NORMAL DISTRIBUTION: Features: (1)It is completely characterized by just two parameters i.e. , expected return and standard deviation of return.(2)A bell-shaped distribution, it is perfectly symmetric around the expected return.(3)The probabilities for values lying within certain bands are : Band Probability + One Standard Deviation 68.3% + Two Standard Deviation 95.4% + Three Standard Deviation 99.7% RISK AVERSION AND REQUIRED RETURNS:(1)The relationship of a person’s certainty equivalent to the expected monetary value of a risky investment defines his attitude toward risk. If the certainty equivalent is less than the expected value, the person is risk-averse; if the certainty equivalent is equal to the expected value, the person is risk-neutral; finally, if the certainty equivalent is more than the expected value, the person is risk-loving.(2)In general, investors are risk-averse. This means that risky investments must offer higher expected returns than less risky investments to induce people to

invest in them. Remember, however, that we are talking about expected returns; the actual return on a risky investment may well turn out to be less than the actual return on a less risky investment. (3)Put differently, risk and return go hand in hand. This indeed is a well-established empirical fact, particularly over long periods of time.

EXPECTED RETURN ON A PORTFOLIO: is the weighted average of the expected returns on the assets comprising the portfolio. When a portfolio consists of two securities the expected return is , E(Rp) = w1* E(R1)+(1-w1) * E(R2) where, E(Rp) = expected return on a portfolio, w1=proportion of a portfolio invested in security 1,E(R1)=expected return on a security...