# Risk and Return

**Topics:**Capital asset pricing model, Modern portfolio theory, Normal distribution

**Pages:**9 (3586 words)

**Published:**July 30, 2013

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...

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