Risk And Returns PDF

**[RISK AND RETURNS]** 1. **[Measures of Risk]** Measuring of risk means quantifying it in terms of number, this can be done by using various 'Measures of Risk;' various measures of risk covered by BMS portion are: - Range - Variance - Standard Deviation - Co-efficient of...

**[RISK AND RETURNS]** 1. **[Measures of Risk]** Measuring of risk means quantifying it in terms of number, this can be done by using various 'Measures of Risk;' various measures of risk covered by BMS portion are: - Range - Variance - Standard Deviation - Co-efficient of Variation **Range** Range refers to the spread of the various possible future returns, in other words, range refers to the difference between the highest possible return and lowest return expected from the security. It is the percentage between which the future returns are expected to fluctuate, *higher the fluctuation higher is the risk and therefore higher the range higher is the risk.* **Range = highest returns -- lowest return.** **Variance** We compare every possible return with the average or expected return of the security, doing so we get how far are all the possible returns lying from the expected returns (i.e. Level of variance of all possible returns from the average), after calculating the same of all the possible returns, the numbers so calculated are squared to convert any negative numbers into positive numbers, the number So squared are added to get 'variance' in totally **Variance (without probabilities)** **Var = [(xi−¯x)2]** **n** **Variance (with probabilities)** **Var = ∑P ^(^xi −¯x)^2^** **Standard Deviation** Standard deviation is nothing nut square root of Variance. In terms of Formula Standard Deviation is denoted as Follow: **(Without probabilities)** **∂= √[(xi−¯x)^2^] OR ∂ = √variance** **^n^** **(With probabilities)** **∂ = √∑P ^(^xi −¯x)^2^ OR ∂ = √variance** **II. TYPES OF RISK** **SYSTEMATIC RISK** A risk that affects the whole economic system and all the industries operating in the economic system in a systematic manner is known as systematic risk, these kind of risk affects the price of all the securities. The effect of systematic return causes the prices of all individual shares/bonds to move in the same direction. E.g.: change in political situation of nation, war, change in government policy to discourage free capital markets, high degree of inflation etc. As can be seen from preceding examples, this risk will affect income generating capacity of all the companies in the economy and hence systematic risk cannot be avoided. As systematic risk affects all the companies, it cannot be eliminated by even by diversification of portfolio it is also called unavoidable risk. This type of risk will arise due to the following reason: **Market price:** Variations in price sparked off due to social, political, & economic events is referred to a market risk. **Interest Rate Risk:** The uncertainty of future market values & the size of future incomes, caused by fluctuations in the general level of interest is known as Interest Rate Risk. **Purchasing Power Risk:** Uncertainties of purchasing power is referred to as risk due to inflation. If investment is considered as consumption sacrificed, then a person purchasing securities foregoes the opportunities to buy some goods or services for so long as he continues to hold the securities. In case, the prices of goods and services, increases during the period, the investor loses purchasing power. **UNSYSTEMATIC RISK** Risk that affects specific companies or firms instead of the whole economic or market system is known as Unsystematic risk, this risk is company specific risk. The Unsystematic risk is the change in the price of stocks due to the factors which are particular to the stock. Normally such a risk for one company creates and earning opportunity for some other company or industry therefore as far as unsystematic risk is concerned loss of one company normally means profit of some other company. Therefore, systematic risk can be eliminated or reduced by scientific diversification of portfolio in such stocks whose income behaves in opposite direction than compared with each other. This is the reason this risk is also called **avoidable risk.** The unsystematic risk will arise due to the following reasons: **External Business Risk:** External business risk arises due to change in operating conditions caused by conditions thrust upon the firm which are beyond its control such as business cycles government controls etc. **Internal Business Risk:** Internal business risk is associated with the efficiency with which a form conducts its operations within the broader environment imposed upon it. **Financial Risk:** financial risk is associated with the capital structure of a firm. A firm with no debt financing has no financial risk. The extent of financial risk depends on the leverage of the firm's capital structure. **TYPES OF RISK TAKERS/ INVESTORS LIKING FOR RISK** Commonly investors will have 3 attitudes to undertake risky courses of actions 1. An aversion to risk, 2. A desire to take risk s3. An indifference to risk **Risk Averse Investors:** A rational investor would always like to maximize his returns at minimum risk. This category of investor likes to avoid taking risk he does not like to take extra risk if he is offered same level of expected returns. He will take extra risk only if he is offered extra returns by investing in a risky security. Normally all investors are risk avoid because no one would like to incur extra risk for earning same of returns. **Risk taking investors**: These are those investors who like to take more risk, their main motive while investing money is not to earn returns but to take risk. They like to take high risk with investing the funds available to them in risky investments to satisfy their urge to take risk and hope of earnings huge returns. **Risk indifferent investors**: this category of investors is not concerned with the level of risk they take by investing money in a particular investment Avenue. **Illustration 1: -** Given below are the likely return in case of shares of Ram Ltd. and Krishna Ltd. in the various economic conditions. **Economic Condition** **Probability** **Return (%) of Ram Ltd.** **Return (%) of Krishna Ltd.** ------------------------ ----------------- ---------------------------- -------------------------------- High Growth 0.3 15% 10% Low Growth 0.4 13% 11% Stagnation 0.2 9% 12% Recession 0.1 6% 14% a. Calculate the expected rate of return and standard deviation of return on stock of Ram Ltd. and Krishna Ltd. b. If you could invest in either stock of Ram Ltd. or Krishna Ltd., but not in both which stock would you choose? **Illustration 2: -** **[Company P]** **[Company Q]** ----------------------------- ----------------------------- ------------ ----------------- **Return** **Probability** **Return** **Probability** **(%)** **(%)** **(%)** **(%)** 6 0.10 4 0.1 7 0.25 6 0.2 8 0.30 8 0.4 9 0.25 10 0.2 10 0.10 12 0.1 **Illustration 3: -** **State of Nature** **Probability** **Return on Fixed Asset "A"** **Return on Fixed Asset "B"** --------------------- ----------------- ------------------------------- ------------------------------- 1 0.1 5% 0 2 0.3 10% 8% 3 0.5 15% 18% 4 0.1 20% 26% 1. What is the standard deviation of the return on Fixed Asset "A" and "B"? 2. What is the covariance between the returns on both the Fixed Assets? 3. What is the coefficient of correlation between the returns on Fixed Asset "A" and "B"? **Illustration 4: -** +-----------+-----------+-----------+-----------+-----------+-----------+ | | 2003-04 | 2004-05 | 2005-06 | 2006-07 | 2007-08 | +===========+===========+===========+===========+===========+===========+ | Mr. | 6% | 48% | -15% | 7% | 11% | | Narendra | | | | | | | | 12% | 40% | -6% | 20% | 3% | | Sensex | | | | | | +-----------+-----------+-----------+-----------+-----------+-----------+ Calculate the average return and standard deviation of Mr. Narendra's Mutual Fund. Did he do better or worse than Sensex by these measures? **Illustration 5**: - Following is information about shares of PQR Ltd. and KLM Ltd. under different economic condition. At present both shares are traded at Rs. 100 **Economic Condition** **Probability** **[Expected Price of Share]** ------------------------ ----------------- ------------------------------------------- -------------- **PQR Ltd.** **KLM Ltd.** High Growth 0.3 Rs. 140 Rs. 150 Low Growth 0.4 Rs. 110 Rs. 100 Stagnation 0.2 Rs. 120 Rs. 120 Recession 0.1 Rs. 100 Rs. 80 i. Which company has more risk to invest? ii. Ms. Shanti want to invest Rs. 10,000. a. Only in PQR Ltd. (**b)** Only in KLM Ltd. **Illustration 6: -** X Ltd and Y Ltd. has the following risk and return estimates: RA=20% RB=22% σA=15 σB=18 Cor (A, B) = -1 Calculate the risk and return of the portfolio consisting of 55% of X Ltd. and 45% of Y Ltd. **Illustration 7: -** The rate of return of stock "S" and "T" under different status of economy are given below: **Particular** **Boom** **Normal** **Recession** --------------------- ---------- ------------ --------------- Probability 0.30 0.50 0.20 Return on stock "S" 30.0 50.0 70.0 Return on stock "T" 70.0 50.0 30.0 a. Calculate the expected return and standard deviation of return on both the stock. b. If you could invest in either stock "S" or stock "T", but not in both which stock would you prefer? **Illustration 8: -** Given below are the likely returns in case of Share of Moon Ltd. under various economic conditions. **Economic Condition** **Probability** **Return (%)** ------------------------ ----------------- ---------------- Boom 0.25 7 Low Growth 0.25 10 Stagnation 0.30 14 Recession 0.20 19 Calculate expected return and standard deviation. **Illustration 9: -** Radha has been considering an investment in stock A and B. she estimated the following Probability distribution of return of stock A and stock B. **Return on Stock A** **Return on Stock B** **Probability** ----------------------- ----------------------- ----------------- -10 5 10 0 10 25 10 15 40 20 20 20 30 25 05 Calculate the expected return and Standard deviation of stock A and B. State which stock is worth investing. **Illustration 10: -** The rate of return on stocks of Star Ltd. and King Ltd. under different states of economy are presented below along with Probability of the occurrence of each state of the economy. **Particular** **Boom** **Normal** **Recession** ------------------------------------------ ---------- ------------ --------------- Probability 0.3 0.4 0.3 Rate of return on stock of Star Ltd. (%) 40 60 80 Rate of return on stock of King Ltd. (%) 90 60 40 Calculate the expected rate of return and standard deviation of return for both companies. Also advise investor for his decision of investment. **Illustration 11: -** PQ Ltd. stock currently pays no dividends and is currently selling at Rs. 90. The possible prices for which the stock might sell at the end of the year with associate probabilities are: **End of year Price (Rs.)** **Probability** ----------------------------- ----------------- 100 0.1 110 0.2 120 0.4 130 0.2 140 0.1 Calculate the expected rate of return for the year end. **Illustration 12: -** The rate of return of Stock X and Y under different states of economy are presented below along with the probability of the occurrence of each state of the economy. **Boom** **Normal** **Recession** ------------------------------- ---------- ------------ --------------- Probability of occurrence 0.3 0.4 0.3 Rate of return on stock X (%) 20.0 30.0 50.0 Rate of return on stock Y (%) 50.0 30.0 20.0 a. Calculate the expected rate of return and standard deviation of return for stock X and stock Y. b. If you could invest in either stock X or stock Y, but not in both, which stock would you prefer? c. Would your preference in question **(b)** above change, if following changes are made in rate of return on stock X? **Boom** **Normal** **Recession** ------------------------------- ---------- ------------ --------------- Rate of return on stock X (%) 50 40 30 **Illustration 13: -** Consider two risky assets C and D: - **Security** **Expected Return** **Standard Deviation** -------------- --------------------- ------------------------ **C** 20% 10% **D** 30% 20% Correlation (C and D) = 0.4 Calculate Expected Return and Standard Deviation of portfolio. **Illustration 14: -** The rate of return of stocks M and N under different status of economy are given below: **Economy** **Probability** **Return of Stock M (%)** **Return of Stock N (%)** ------------- ----------------- --------------------------- --------------------------- Boom 0.3 35 15 Normal 0.5 25 25 Recession 0.2 15 35 i. Calculate the expected rate of return and standard deviation of return of both the stocks. ii. If you could invest in either stock M or N but not in both, which stock would you prefer? **Illustration 15: -** The Analyst has provided you the following estimates in respect of equity shares of Y Ltd. and Z Ltd. **Security** **Y Ltd.** **Z Ltd.** ------------------------- ------------ ------------ Expected Rate of Return 30% 28% Standard Deviation 8% 7% The correlation coefficient between Y Ltd. & Z Ltd. is 0.4. Assuming equal amount of funds invested in both the Securities estimate the standard deviation of the portfolio. 1. Ms. Jyoti purchased 10 shares of Xavier Ltd. On 01/01/2022 for Rs 75 per share, during the year 2009 Xavier ltd paid dividend of Rs 12 per share. The market price of the share on 31/12/2009 was Rs 93 per share. You are required to find out the returns earned by Ms. Jyoti during the year 2022. (Ans. 40%) 2. Mr. X purchased 5 shares of Multan Ltd. For 57rs each on 01/04/2020, during the year company paid a dividend of 4rs per share. Mr. X sold the shares on 31/03/2021 for 50rs each. You are required to find out the returns earned by makes during the year. (ans. -3.51%) 3. Jones purchased 12 shares of Liverpool Ltd. For Rs 190 per share on 01/01/2020. During the time span of 3 years Liverpool Ltd paid the following dividends per share 2020- Rs7, 2021- Rs9, 2022- Rs12. Jones sold the shares on 31/12/2022 for Rs225 per share, find out the holding period returns earned by jones. (Ans. 33.16%) (Ans. 11.053%) 4. ABC Ltd. Paid the following dividend per share and had the following market price per share during the period 2004-09. Year Dividend per share Market price per share ------ -------------------- ------------------------ 2004 1.53 31.25 2005 1.53 20.75 2006 1.53 30.88 2007 2.00 67.00 2008 2.00 100.00 2009 3.00 154.00 Calculate the annual rate of return for the last 5 years. 5. XYZ ltd. Paid the following dividend per share and had following market price per share during the period 2001-04. Year Dividend per share Market price per share ------ -------------------- ------------------------ 2001 7 95 2002 9 105 2003 11 90 2004 12 158 Calculate the annual rate of return for last 3 years. **(With probabilities)** **For security X, Y & Z from following information:** Situation Probability (P) Returns (%) ----------- ----------------- ------------- ---- ----- X Y Z Boom 0.15 24 30 40 Normal 0.50 16 20 25 Recession 0.35 8 -8 -10 **For security Zen, Ken & Pen from following information:** Situation Probability (P) Returns (%) ----------- ----------------- ------------- ----- ----- Zen Ken Pen Recession 0.20 15 -25 -45 Normal 0.60 25 35 40 Boom 0.20 40 50 55 **Given below are the returns for shares of KSS Ltd. And GSS Ltd. In the various economics conditions. Both the shares are presently quoted at Rs.250 per share.** +-----------------+-----------------+-----------------+-----------------+ | Economic | Probability | Returns of | Returns of | | Conditions | | | | | | | KSS Ltd (%) | GSS Ltd (%) | +=================+=================+=================+=================+ | High Growth | 0.25 | 110 | 180 | +-----------------+-----------------+-----------------+-----------------+ | Low Growth | 0.25 | 130 | 150 | +-----------------+-----------------+-----------------+-----------------+ | Stagnation | 0.30 | 160 | 100 | +-----------------+-----------------+-----------------+-----------------+ | Recession | 0.20 | 190 | 70 | +-----------------+-----------------+-----------------+-----------------+ 1. Which of the companies is risky investment? 2. Mr. Suraj has Rs.2000 and wants you to recommend one of the above two shares for investment. 3. Would your answer change if the probabilities change to 0.10, 0.20, 0.30, and 0.40 for various economic seniors. The rate of return on stock A and N, under different states of the economy are given below:   Boom Normal Recession ------------------------------- ------ -------- ----------- Probability of occurrence 0.30 0.50 0.20 Rate of return on stock A (%) 30 50 70 Rate of return on stock N (%) 70 50 30 1. Calculate the expected return and standard deviation of return on both the stock. 2. If you could invest in either stock A or N, but not in both, which stock would you prefer? 3. What would be your decision if the probabilities changed to 15:15:70? The rate of return on stocks of MCC & NCC under different states of the economy are presented below along with the probability of the occurrence of each state of the economy.   Boom Normal Recession ---------------------------------- ------ -------- ----------- Probability of occurrence 0.30 0.40 0.30 Rate of return on stocks MCC (%) 40 60 80 Rate of return on stock NCC (%) 80 60 40 1. Calculate the expected return and standard deviation of return on both the stock. 2. If you could invest in either stock MCC or NCC, but not in both, which stock would you prefer? 3. If the rate of return on MCC was revised as shown below, would your preference in questions (b) above change? Why? **(WITHOUT PROBABILITIES)** From the information given below find out returns and standard deviation for ABC ltd. Year R~ABC~ ------ -------- 2005 -28.7 2006 56.19 2007 123.45 2008 54.24 2009 57 From the information given below find out returns and standard deviation for XYZ ltd. Year R~XYZ~ ------ -------- 2005 25 2006 45 2007 60 2008 40 Calculate expected returns from the following information for GEC ltd. Month Returns ----------- --------- January 0.034 February -0.06 March -0.118 April 0.067 May -0.063 June -0.079 July -0.059 August 0.268 September 0.178 October 0.191 November -0.071 December -0.055 Calculate expected returns from the following information for GEC Ltd. Month Returns ---------- --------- January 0.04 February 0.09 March -0.06 April 0.075 May -0.05 June 0.08 **\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#\#**