...Risk and return will be very central terms in our analysis and it is essential that the reader clearly understands the meaning of each term and how assets with different payout structures can be compared. General utility theory suggests that the average investor is risk averse. Given the same expected return of two assets with different risks, he would prefer the one with less risk. (This assumption may not be perfectly true for all individuals in all situations, but for the investor community as a whole it is probably true). For an asset with uncertain cash flows and payoffs, which are normally distributed, the mean of the distribution will be the expected return while the standard deviation forms some kind of “risk”. Choosing the “less risky” asset therefore comes down to choosing the asset with the lowest standard deviation in its payout distribution. An investor could also approach the problem from the other direction, choosing among assets with the same risk and then choose the asset with the highest expected return. Risk is usually defined as the volatility of returns, measured by standard deviation. The variance of a portfolio depends not only on the individual variances of the as- sets, but also on the co-variances between the components of the portfolio. As an extreme example, a portfolio consisting of two securities – a long position in a stock and with an appropriately chosen position in a put option on the same stock – will have lower...
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...RISK AND RETURN Risk is existing in every business decision. For Eg: Selection of an asset for production department, developing a new product etc., Therefore decision maker has to asses the risk and return before taking any financial decision. To do so finance manager must learn to assess risk and return. Risk can be measured in different ways. Before going to learn the computation and return it is require understanding the followings: 1. Cash Flows: financial assets are expected to generate cash flows and risk of Financial assets assessed in terms of the variations of its expected cash inflows. 2. Risk can be measured either on stand alone basis or in a portfolio context 3. Classification of risk: the risk of assets is divided into two parts. a. Diversifiable Risk b. Market Risk. Diversifiable risk is a company’s’ specific risk and can be completely eliminated through diversification. On the other hand market risk arises from market movements and which cannot be eliminated through diversification. 4. Investors are Risk Averse: (unwilling/opposed) Generally investors are risk averse. It does not mean that investors do not buy risk assets, they buy risk assets, when they promise extra return for bearing extra risk. Risky investments provide relatively high return. Risk: Risk is the chance of financi8al loss or the variability of returns associated with a given assets. Assets that are having higher chances of loss ar viewed as more risky...
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...Exercises E8-1. Total annual return Answer: ($0 $12,000 $10,000) $10,000 $2,000 $10,000 20% Logistics, Inc. doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. E8-2. Expected return Answer: Analyst 1 2 3 4 Total Probability 0.35 0.05 0.20 0.40 1.00 Return 5% 5% 10% 3% Expected return Weighted Value 1.75% 0.25% 2.0% 1.2% 4.70% E8-3. Comparing the risk of two investments Answer: CV1 0.10 0.15 0.6667 CV2 0.05 0.12 0.4167 Based solely on standard deviations, Investment 2 has lower risk than Investment 1. Based on coefficients of variation, Investment 2 is still less risky than Investment 1. Since the two investments have different expected returns, using the coefficient of variation to assess risk is better than simply comparing standard deviations because the coefficient of variation considers the relative size of the expected returns of each investment. E8-4. Computing the expected return of a portfolio Answer: rp (0.45 0.038) (0.4 0.123) (0.15 0.174) (0.0171) (0.0492) (0.0261 0.0924 9.24% The portfolio is expected to have a return of approximately 9.2%. E8-5. Calculating a portfolio beta Answer: Beta (0.20 1.15) (0.10 0.85) (0.15 1.60) (0.20 1.35) (0.35 1.85) 0.2300 0.0850 0.2400 0.2700 0.6475 1.4725 E8-6. Calculating the required rate of return Answer: a. Required return 0.05 1.8 (0.10 0.05) 0.05 0.09 0.14 b. Required return 0.05 1.8 (0.13 0.05) 0.05 0.144 0.194 c. Although the risk-free rate does not change...
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...Return, Risk and The Security Market Line - An Introduction to Risk and Return Whether it is investing, driving or just walking down the street, everyone exposes themselves to risk. Your personality and lifestyle play a big role in how much risk you are comfortably able to take on. If you invest in stocks and have trouble sleeping at night, you are probably taking on too much risk. (For more insight, see A Guide to Portfolio Construction.) Risk is defined as the chance that an investment's actual return will be different than expected. This includes the possibility of losing some or all of the original investment. Those of us who work hard for every penny we earn have a hard time parting with money. Therefore, people with less disposable income tend to be, by necessity, more risk averse. On the other end of the spectrum, day traders feel that if they aren't making dozens of trades a day, there is a problem. These people are risk lovers. When investing in stocks, bonds or any other investment instrument, there is a lot more risk than you'd think. In this section, we'll take a look at the different kind of risks that often threaten investors' returns, ways of measuring and calculating risk, and methods for managing risk. Expected Return, Variance and Standard Deviation of a Portfolio Expected return is calculated as the weighted average of the likely profits of the assets in the portfolio, weighted by the likely profits of each asset class. Expected return is calculated...
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...Chapter 5 Risk and Return 5.1 RATES OF RETURN McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Learning objectives Use data on the past performance of stocks and bonds to characterize the risk and return features of these investments Determine the expected return and risk of portfolios that are constructed by combining risky assets with risk-free investment in Treasury bills Evaluate the performance of a passive strategy McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Holding Period Return The holding period return (HPR)(보유기간수익률) Depends on the increase (or decrease) in the price of the share over the investment period as well as on any dividend income. Rate of return over a given investment period McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Example 5.1 Suppose you are considering investing some of your money, now all invested in a bank account, in a stock market index fund. The price of a share in the fund is currently $100, and your time horizon is one year. You expect the cash dividend during the year to be $4, so your expected dividend yield is 4%. Your HPR will depend on the price one year from now. Suppose your best guess is that it will be $110 per share. The your capital gain will be $10 (110-100), so your capital gains yield is $10/$100=.10 or 10%. The total holding period rate of return is the sum of the dividend...
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...Period Return HPR=(Ending price-Beginning price+Dividend during period one)/(Beginning price)=(P_1-P_0+D_1)/P_0 Dividend Yield: % return from dividends Expected Return and Standard Deviation E(r)=∑_s▒〖p_s r_s 〗 σ=√(∑_s▒〖p_s (r_s-E(r))〗^2 ) Expected end-of-year value of the investment =Dividend+Ending Price Arithmetic and Geometric Averages Arithmetic Mean (AM) =(∑▒HPR)/N Better predictor of future performance Geometric Mean (GM) = π(1+HPR) )^(1/N)-1 Better measure of past performance GM < AM Sharpe Ratio Sharpe Ratio for Portfolios =(Excess Return)/(SD of Excess Return)=(R_i-R_f)/(σ(R_i-R_f)) Measure the attraction of an investment portfolio by comparing its reward (risk premium) and risk (SD) Excess return per unit of risk Reward-to-variability (volatility) ratio Historical Returns on Risky Portfolios Asset classes that provide higher return are more risky Return: Small Stocks > Large Stocks > Bonds > Bills Risk: Small Stocks > Large Stocks > Bonds > Bills Risk Premium Extra reward (returns) for bearing the risk of investing in equities, rather than in low risk investments, such as bills or bonds Risk Premium=E(r)-r_f Asset Allocation: Four Step Process Step 1: Assessing Risk Tolerance Step 2: Measuring Portfolio Risk and Return Step 3: Modeling Investment Options Step 4: Optimal Asset Allocation Step 1: Assessing Risk Tolerance Dominated Assets Easy to remove from consideration Always choose higher risk premium...
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...Risk and Return Concepts Prepared by: JQY Risk and Return Concepts • Measures of risk and returns • Portfolio risk and returns • CAPM Return – what is earned on an investment: the sum of income and capital gains generated by an investment. Risk – possibility of loss; the uncertainty that the anticipated return will not be achieved. Risk and Return? If you have PHP 1,000,000, will you invest in: 5% 20% Risk and Return General Rule of Thumb: More Risk = More Returns Less Risk = Less Returns It depends on the investor: Risk Seeking – prefers high risk investments Risk Neutral – willing to take on moderate risk Risk Averse – conservative, unwilling to take on high risk investments unless the returns justify and compensates for the high risk taken. Relative Risk & Returns of Asset Classes Source: http://www.weblivepro.com/articles/cpp/cppinfo.aspx Measures of Returns • Historical Returns ▫ Holding Period Return ▫ Alternative Measures Arithmetic Mean Geometric Mean Harmonic Mean • Expected Returns Measuring Historical Returns • Holding Period Return ▫ Total return on an asset or portfolio over the period during which it was held ▫ HPR = MV1 – MV0 + D MV0 MV1 = market value, end MV0 = market value, beginning D = cumulative cash distributions (at the end of period) • Annualized HPR ▫ (1 + HPR) ^ 1/n – 1 Measuring Historical Returns • Example: Mr. A bought an asset in 2005 for P100. He kept it...
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...Valuation, Risk, and Return Five years ago, Laissez-Faire Recliners issued $10,000,000 of corporate bonds with a 30-year maturity. The bonds have a coupon rate of 10.125%, pay interest semiannually, and have a par value of $1,000 per bond. The bonds are currently trading at a price of $879.625 per bond. A 25-year Treasury bond with a 6.825% coupon rate (paid semi-annual) and $1,000 par is currently selling for $975.42. In order to find the yield spread between the corporate bonds and the Treasury bonds we must first find the yields of both bonds. The yield is the amount of return an investor can expect to receive from a bond. The yield for the corporate bond (found using the yield formula in excel) is 11.57%. The yield for the Treasury bond is 7.04%. The yield spread is found by adding these two percentages and finding the average (dividing by 2), in this case the yield spread is 9.30%. If you are considering an investment in Laissez-Faire’s bonds (that will be held to maturity) and require an 11% rate of return you would not invest in these bonds. You would invest solely in the corporate bonds, however that is not an option, so you would bypass this option since the bond yield falls below this 11% required rate of return. If you are considering a purchase of Laissez-Faire’s preferred stock, with a current market price of $42, a par value of $50, and a dividend amounting to 10% of par, you must calculate the actual value of the stock. In this case it falls at $40, which...
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...Risk & Return Analysis: Analyzing an equally weighted portfolio of investments in Amazon, Inc., Yahoo! Inc., and Direct TV stock compared to the S&P 500 Introduction: Every day, millions of investors spend countless hours following the stock market in the hopes of striking it rich. Making the right moves at the right moments is crucial when one looks to make large returns in the market. While luck affords many investors the opportunity to make lucrative returns in the stock market, this reward does not come without risk. In order to balance their returns and the amount of risk that they are exposed to, many investors create an investment portfolio as a means to mitigate risks in the market at the expense of foregoing potentially higher returns on their investment. To illustrate the effects that a diversified portfolio can have on the amount of risk an investor takes on as well as the returns that the investment generates, a sampling of three random stocks and the S&P 500 index was created to examine the effects that diversification has on investment risk. Investments: For this analysis, monthly stock data from December 1, 2009 – December 1, 2014 was compiled on three stocks and the S&P 500. The three investments chosen for the portfolio were Amazon.com Inc. (AMZN), Yahoo! Inc. (YHOO), and DirectTV. (DTV), and each represent 25% of the portfolio. In order to analyze the risks associated with each stock, a Risk-Free rate of interest must be established in order...
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...is expected return considered forward-looking? What are the challenges for practitioners to utilize expected return?" (Cornett, Adair, & Nofsinger, 2016, p. 258). Expected return is considered “forward-looking” because it is the return investors expect to receive in the future. This comes in the form of compensation for the market risk taken. The challenge that practitioners face in utilizing expected return is not being able to precisely know what the future holds. Therefore, methods to estimate the expected return are created. * Distinguished-level: Explain the role of probability distribution in determining expected return. * Question 2: * Proficient-level: "Describe how different allocations between the risk-free security and the market portfolio can achieve any level of market risk desired" (Cornett, Adair, & Nofsinger, 2016. p. 258). An investor can allocate money between a risk-free security that has zero risk (β=0), and the market portfolio that has market risk (β=1). If 75% of the portfolio is invested in the market, then the portfolio will have a β=0.75. If only 25% is invested in the market, then the portfolio will have a market risk of β=0.25. * Distinguished-level: Provide examples of a portfolio for someone who is very risk averse and for someone who is less risk averse. The first example (β=0.75) might be taken by a less risk averse investor while the second example (β=0.25) illustrates the portfolio of a more risk averse investor...
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...Financial Risk: Key Fundamentals and Case Studies Leonard Chumo, CFA, FRM Strathmore University GARP Chapter Meeting 29th July 2011 Agenda 1. Background 2. Credit Risk and the Case of Washington Mutual 3. Operational Risk and the Case of Rogue Brokers in Kenya and Barings 4. Market Risk and the Case of LTCM 5. Liquidity Risk and the Case of Northern Rock 6. Q&A BACKGROUND Main Types of Financial Risk Risk Type Definition Credit Risk The potential that a bank's borrower or counterparty will fail to meet its obligations in accordance with agreed terms. Market Risk The risk that movements in market prices will adversely affect the value of on- or off-balance sheet positions. The risk is attributable to movements in interest rates, foreign exchange (FX) rates, equity prices or prices of commodities. Operational Risk Risk of loss resulting from inadequate or failed internal processes, people and systems, or from external events. The definition includes legal risk, but excludes reputational and strategic risk. Liquidity Risk Liquidity is the ability to fund increases in assets and meet obligations as they become due. It is crucial to the ongoing viability of any organization. Source: Financial Stability Institute CREDIT RISK AND THE CASE OF WASHINGTON MUTUAL Sources of Credit Risk Apart from traditional types of loans, credit risk can also be found in a bank's: Investment portfolio ...
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...Risk & Return, a trade off What is a risk? Dictionary meaning of risk could be exposure, hazard, uncertainty, and chance. It conveys a negative sense like possibility of incurring loss or misfortune or injury. It is the probability that a hazard may turn into a disaster or, in other words, the probability that a disaster may happen. Fortunately, risk can be foreseen and managed by various ways such as (i) passing it on to others through insurance, guarantees and sub-contracting, (ii) sharing it by formation of consortium or syndicates, or (iii) reducing it by diversification of possessions or portfolio. What is a return? It means compensation, gain, income, reward, pay off or yield. It would be notice that the word ‘return’ conveys a positive sense as against the word ‘risk’ which forewarns of dangers. Risk & Return Trade Off When one says high risk, high returns, it means that chance of getting high returns are most uncertain or lower. To be blunt, an investor can get high return if he or she is willing to sustain a total losse like in a lottery. One may purchase a share in the stock-exchange in the hope of making a big profit over a short period of time. This is not investing but gambling as there is no guarantee that one will get the desired returns. Some shares in the past have shown a tremendous growth but such occurrences are rare. Source: wikipedia.org Risk & Return Two Major Investment Soundness Indicators 1 - Internal Rate of Return...
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...Risk and Return Tradeoff Memo The construction portfolio process concludes to be very complex. Statistical past performance, industry knowledge, future potential and relying on insights that are personal are typically what analysts rely on within the market in order to arrive at the final list. Maximizing returns while minimizing risk is the goal every investor aims for. An evaluation of individual securities as well as risk return trade off within isolation and the risk return trade off contribution of the entire portfolio. The managing and constructing of a portfolio simulation outlining the fundamentals within the construction of the portfolio in regards to the risk return trade off as well as the relationship among investment performance and strategy will be the structure of this memo. Casa Bonita Ceramics has selected me as the treasury analyst to determine the best stocks and allocate company resources in order to construct a successful portfolio. My decision will be detailed within this memo of the simulation, communicate the Sharpe ratio in the relation it has to investment decision as well as give recommendations for organization changes in the investment strategy to improve the investment performance. Simulation Decisions Given the excess cash generated in the previous year, Casa Bonita is considering the invest $800,000 in the stock market. Eight stocks have already been chosen. Given the high return consideration without the risk of capital loss in sight, narrowing...
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...CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD PROBLEM SETS 1. The Fisher equation predicts that the nominal rate will equal the equilibrium real rate plus the expected inflation rate. Hence, if the inflation rate increases from 3% to 5% while there is no change in the real rate, then the nominal rate will increase by 2%. On the other hand, it is possible that an increase in the expected inflation rate would be accompanied by a change in the real rate of interest. While it is conceivable that the nominal interest rate could remain constant as the inflation rate increased, implying that the real rate decreased as inflation increased, this is not a likely scenario. 2. If we assume that the distribution of returns remains reasonably stable over the entire history, then a longer sample period (i.e., a larger sample) increases the precision of the estimate of the expected rate of return; this is a consequence of the fact that the standard error decreases as the sample size increases. However, if we assume that the mean of the distribution of returns is changing over time but we are not in a position to determine the nature of this change, then the expected return must be estimated from a more recent part of the historical period. In this scenario, we must determine how far back, historically, to go in selecting the relevant sample. Here, it is likely to be disadvantageous to use the entire dataset back to 1880. 3. The true statements...
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...Assessing the risk, return and efficiency of banks’ loans portfolios ∗ Javier Menc´ ıa Bank of Spain June 2008 Preliminary and Incomplete Abstract This paper develops a dynamic model to assess the risk and profitability of loans portfolios. I obtain their risk premia and derive the risk-neutral measure for an exponentially affine stochastic discount factor. I employ mean-variance analysis with a VaR constraint to assess efficiency. Then I compare Spanish institutions in an empirical application, where small institutions seem to be less efficient than large ones on aggregate terms, while commercial and savings banks perform better on their respective traditional markets. Finally, I find increasing discrepancies between riskneutral and actual default probabilities since June 2007 and discuss their possible sources. Keywords: Credit risk, Probability of default, Asset Pricing, Mean-Variance allocation, Stochastic Discount Factor, Value at Risk. JEL: G21, G12, G11, C32, D81, G28. This paper is the sole responsibility of its author. The views represented here do not necessarily reflect those of the Bank of Spain. Thanks are due to Alfredo Mart´ for his valuable suggestions as well as for ın, help with the interest rate database. Of course, the usual caveat applies. Address for correspondence: Alcal´ 48, E-28014 Madrid, Spain, tel: +34 91 338 5414, fax: +34 91 338 6102. a ∗ 1 Introduction Standard capital market theory states that there is a risk-return tradeoff in equilib- ...
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