The document discusses risk and return related to financial assets. It defines return as the total gain from an asset including price changes and cash payments. Risk is the variability between actual and expected returns, with greater chances of loss seen as riskier. Managers have different risk preferences such as being risk indifferent, risk averse, or risk seeking. Risk is computed using methods like standard deviation, which measures dispersion around the expected return. There are systematic risks that influence many assets, like interest rates, and unsystematic risks that are specific to individual assets. Diversification reduces unsystematic risk. The capital asset pricing model relates risk premium to an asset's beta, or systematic risk relative to the market.

1. Risk & Return

2. RETURN – The Return from holding a Financial Asset over a specified period can be defined as the total gain earned in the form of cash payments received due to ownership and any change in market price of the Asset divided by the beginning price. RISK – The Risk is the variability of Returns from those that are expected. The difference between actual and expected return is the source of Risk. It is the chance of financial loss. Assets having greater chances of loss are viewed as more risky than those with lesser chances of losses. RISK PREFERENCES – Managers and Firms have different risk preferences: Risk Indifferent Managers – Required or expected return does not change as risk changes. Risk averse Managers – Required or expected return increases as risk increases. Risk seeking Managers – Required or expected return decreases as risk increases.

3. COMPUTATION OF EXPECTED RATE OF RETURN The expected rate of return E(R) is the weighted average of all possible returns multiplied by their respective probabilities. COMPUTATION OF RISK Risk is computed for any financial assets as (i) asset being the standalone asset and/or (ii) asset being the part of a portfolio. The risk can be assessed in following manner: SENSITIVITY ANALYSIS – It uses several possible-return estimates to obtain a sense of the variability among outcomes. One common method involves making pessimistic (worst), most likely (expected), and optimistic (best) estimates of the returns associated with a given asset. In this case ,the asset’s risk can be measured by the range of returns. The range is found by subtracting the pessimistic outcome from the optimistic outcome. The greater the range, the more variability, or risk, the asset is said to have. PROBABILITY DISTRIBUTION – An event’s probability is defined as the chance that the event will occur. A probability distribution is a model that relates probabilities to the associated outcomes. Bar Chart is the simplest type of probability distribution but it shows only a limited no of outcomes. For all the possible large no of outcomes, continuous probability distribution is used.

4. RISK MEASUREMENT FOR STANDALONE ASSET STANDARD DEVIATION – It measures the dispersion around the expected return. The expected return is the most likely return on an asset. Investment with higher returns have higher standard deviation because higher standard deviation are associated with greater risk. The relationship reflects risk aversion by market participants, who require higher returns as compensation for greater risk. COEFFICIENT OF VARIANCE (Variation) – Coefficient of variance (Variation) is the standard deviation divided by the expected return. TYPES OF RISK SYSTEMATIC RISK – A SYSTEMATIC RISK IS ONE THAT INFLUENCES A LARGE NUMBER OF ASSETS,EACH TO A GREATER OR LESSER EXTENT.BECAUSE SYSTEMATIC RISK HAVE MARKETWIDE EFFECTS,THEY ARE SOMETIMES CALLED MARKET RISKS. UNSYSTEMATIC RISK – AN UNSYSTEMATIC RISK IS ONE THAT AFFECTS A SINGLE ASSET OR A SMALL GROUP OF ASSETS.BECAUSE THESE RISKS ARE UNIQUE TO INDIVIDUAL COMPANIES OR ASSETS ,THEY ARE SOMETIMES CALLED UNIQUE OR ASSET-SPECIFIC RISK.THESE CAN BE MINIMISED WITH DIVERSIFICATION.

5. Examples of Systematic Risk Change in Interest rate policy, Tax rates. Govt goes for a massive deficit financing. Inflation rate increases. Relaxes foreign exchange control. Examples of unsystematic Risk Company workers declare strikes. R&D Expert leaves the company. Formidable Competitor enters the market. Inadequate/Irregular supply of raw material.

6. The Portfolio Return is the weighted average of return on individual assets. E(R p ) = wE(R 1 ) + (1-w) E (R 2 ) The portfolio Variance/Standard Deviation is not weighted average of the Individual assets’ standard deviation/Variance. The Portfolio Variance/Standard Deviation depends on the co-movement (measured by co-variance) of returns on assets. An Investor has to suffer systematic risk as it cant be diversified away. The difference between variance and co-variance is the diversifiable risk. Unsystematic risk can be eliminated as more securities are added into portfolio. Research show that in USA 15 securities in a Portfolio can eliminate the unsystematic risk while in India this number is 40. Required rate of return on a security is equal to risk free rate plus risk premium for a risky secutity.Risk premium equals the market risk premium, i.e., the difference between expected market return and risk free return. Since market risk premium is same for all securities, the total risk premium varies directly with systematic risk measured by β (Beta).

7. To know the contribution of an individual security to the risk of a well diversified portfolio, the market risk of the security is measured. The market risk of the security is measured by measuring its sensitivity to market movements. This is called as β (Beta). By Definition , β for market portfolio is 1.Any company having β value more than 1 will fluctuate more widely than the market and any company having β value less than 1 will fluctuate less widely than the market . Computation of β Market risk premium is the difference between the return on the market ( r m ) and the risk free return ( r f) . Market risk premium = r m – r f Treasury Bills return is considered as risk free return which is currently 6%-7%.T bills as guaranteed by government have zero risk and hence have zero β .On the other hand market portfolio with a β of 1 will have risk premium as r m – r f. The Capital Asset pricing Model suggests the expected risk premium for a security when β is neither zero or 1. Expected risk premium (r – r f ) = β (r m – r f ) OR , r = β (r m – r f ) + r f Where r = required rate of return on security