1) What are the advantages of the index model compared to the Markowitz procedure for obtaining an efficiently diversified portfolio? Use the case of 80 stocks to illustrate your point.
Answer 1
The benefit of the index model in comparison with the procedure of Markowitz is that the implementation of the index model is way easier. Other than this, the Markowitz process needs the value of standard deviations, expected returns, and covariance for all of the portfolio individual securities. The filing of the covariance matrix is alone in itself a difficult and complex activity requiring a lot of estimations to be made. On the contrary, the index model makes the estimation of the covariance matrix simple by using some assumptions. On the other hand, the procedure of Markowitz also does not allow for the use of the predictions to be used for security risk premiums, which are one of the important points for forecasting the expected returns. Therefore, the index model is much preferred. The benefit of the Markowitz Model is that it takes more measures into consideration while considering the decision making of portfolio allocation. This allows it to be more flexible as compared to the index model. The assumptions used in the index model can lead to more errors as well.
The study by Tanuj and Nivedita worked on constructing an optimal portfolio of 80 stocks. The resulting portfolio selection was based on the formula of excess return to the beta ratio. The study has elaborated on the use of both Markowitz and Index Model and selected the Index model as it was easier and required fewer inputs. The stocks are ranked in order of descending order in terms of the beta ratio. The stocks with the highest excess return to beta ratio were selected in the portfolio (Nandan & Srivastava, 2017).
2) What is the security characteristic line (SCL)? Explain the SCL with respect to figure 8.3. With respect to HPQ (Hewlett Packard), what does the ANOVA table 8.1 suggest about the explanatory effects of the regression equation and also, the explanatory effects of the error term? Discuss the estimate of beta and the firm-specific risk of Hewlett Packard. What is the significance of alpha in the discussion?
Answer 2
The Security Characteristic Line is a line of regression for specific security, which plots the performance of the security against the performance or returns of the market portfolio at different points of time. The Y-axis is based on the value of the excess return of the security above the risk-free return, and the horizontal axis is based on the values of the excess return of the market. The beta is shown by the slope of the line, while the value of the intercept shows the alpha.
Figure 8.3 depicts the SCL for Hewlett Packard Company, showing the performance of the returns of the company against the returns of the S&P 500 Index. In terms of Table 8.1, the table shows the results of regression between the returns of S&P 500 Index and the returns of HP. The ANOVA table particulars provide the information that.
Multiple R: 0.7238 shows a strong positive correlation between the returns of HP and S&P 500 Index.
R-Square: 0.52 shows that around 52% of the points fall on the regression line.
Linear Regression Equation: As per the table, the equation of SCL for HP is;
Y= βx+ α
Y=2.03x+0.0086
Beta shows the risk of the stock as being double that of the market, while the value of alpha shows abnormal returns for the company stock that are very minimal.
3) E believes that all investors should optimize their portfolios a la Markowitz. M, on the other hand, believes that a number of serious challenges exist for E’s contention to be correct and has suggested a labor capital component (a la Mayers) be included. R invokes the theory of Rubinstein, Lucas, and Breeden and believes the foundations of E and extensions of M to be incomplete. Comment on each of their assumptions, challenges, and models.
Answer 3
Markowitz Theory
Assumptions of this theory are based on the notion that market is efficient and the investors have all the knowledge about the market, and this enables them to make prediction about the returns about the stocks based on the past behavior of the returns using the fundamental and technical analysis or by finding the intrinsic value of the stock. It also assumes that the investors have a common goal of avoiding the risk and maximum rate of return. It also assumed that investors base their decisions on the expected returns of a stock. Also, as per this theory, the investor assumes that higher return faces higher risks and the risks can be reduced by adding securities in the portfolio.
As per this model, the efficient set of the portfolio is determined by using the measures of correlation, standards deviation, and returns. The model shows that it is better to hold two securities to reduce the risk than hold one security. The model posits that two securities with negative correlation would reduce the risk of the portfolio.
The Consumption-based asset pricing model has been presented by Lucas, Breeden, and Rubinstein. This is the asset pricing model which is embedded in the stochastic model of macroeconomics. The equations of this model are devolving from the assets and consumption or saving decisions of the households. This model assumes that the economy is made up of a large number of households, which are all identical in their endowments and preferences. This allows the decision making to be analyzed by one representative household. The model assumes that households will never exchange assets. The model needs data on consumption, which is difficult to generate. Other limitations of this model are presented in the form of the reporting of the expenditures as compared to consumptions, infrequent reporting of the stock returns consumption data, sampling errors in consumption values, and the reporting of the integral consumption rates (Breeden, Litzenberger, & Jia, 2015).
Mayer derived the asset pricing model, which incorporated the non-tradable human capital factor as well. This is much like the two-factor ICAPM in which one of the factors is the portfolio of the market, while the other one is the aggregate payoff to the human capital.
4) Ross developed the arbitrage pricing theory (APT) in 1976, while French-Fama followed in 1996 with yet another approach that has become known as the Three Factor Model (FF). Develop a three-slide PowerPoint presentation that differentiates—and labels—multifactor model forms versus a single factor form; articulates the meaning of “arbitrage” in this case (with an numerical example); and generalizes how possibly to employ FF today in an active portfolio and in a 50- security portfolio benchmarked to the S&P 500.
Answer 4
The three most widely used asset pricing models include the CAPM Model, the Arbitrage pricing theory, and the Fama-French Three-Factor Model. The Arbitrage Pricing Theory is a multifactor generalized model, however does not provide any guidance in terms of the appropriate factors which can effectively drive the returns. The French Fama Three-Factor Model describes the risk as the sensitivity of the stock to the three portfolios. These portfolios include the portfolio based on the size of the firm, the stock market and the portfolio, which is based on the book to market ratios. Fama and French in 1992 published a paper that received global attention of the researchers. As per their study, they concluded that the returns of equity are negatively related to the market capitalization of the company and positively related to the ratio of book value to market value of the equity of the company. As per the Arbitrage Pricing Theory, which can be considered as a general version of the Fama multi-factor model. The returns of the security are all specified by the factor of k and the random noise.
It can be shown that with the creation of well-diversified factor portfolios, the expected return of the security should be equal to its exposure to each of the factors and the risk-free rate times the excess returns.
The implementation of this model is vague as there is not much agreement in terms of the number of the factors, their meanings, and their measurement. The arbitrage theory holds that the financial asset expected return can be modeled as per the linear function of the several factors or based on the several market indices in which the factors sensitivity to changes is shown by the specific beta coefficient of the factor.
The French Fama model can be utilized in the current market by using the portfolios which are more titled towards the value stocks than growth stocks, small and middle cap stocks, as compared to the large-cap stocks (Brosch, 2008).
5) Thaler suggests that biases, heuristics, and framing effects routinely plague investor decision making. Give a real-life example in securities analysis, macroeconomic forecasting, and capital budgeting, respectively. How does Thaler support the contention of Shiller (1987)? Perhaps more specifically, what element does Thaler and/or Lakonishok, Shleifer, and Vishny (1995) add to the finance discussion? Express why you agree or disagree with these latter authors.
Answer 5
The framing effect is the principle that shows that the decisions are usually impacted by the way they are communicated or framed with the use of the various settings, wordings, and situations. The mental shortcuts in the shape of the process of the decision making as against the alternative of the analysis and gathering of the information are termed as the heuristics. Behavioral finance has shown the reasons for explaining such behaviors that are against the traditional theories. Common biases that plague the decisions of investors during their securities analysis include the home country bias, the anchoring bias. In terms of Macroeconomic forecasting and capital budgeting, the most common biases are the mental accounting bias and the disposition effects bias. Heuristics examples used for the security analysis can be in the shape of intuitive judgment, in terms of Macroeconomic forecasting and capital budgeting, it can be in the shape of guesstimates and using a rule of thumb. Example of framing effect in terms of securities analysis, Macroeconomic forecasting and capital budgeting can be in the shape of the results of earnings per share for a quarter compared against the past bad performance to show its positive aspect or to compare it against the high expected results to show the negative aspect.
As per the Lakonishok, Shleifer, and Vishny, the investment strategies, which include the purchasing of the value stocks have outperformed the growth stocks over a long period of time. The most likely reason for its working is that the actual future growth rates of the cash flow and earnings of the growth stocks in comparison to the value stock turned out as very low. This shows that the market overestimated the growth of the glamour or the growth stocks and that the value stocks have not been less risky than the glamour stocks. The theory concludes that the value stocks have been underpriced while the glamour stocks had been overpriced. The paper identified that investors had been expecting and investing in growth stocks expecting it to grow based on their past growth despite looking at their future potential showing the pattern of expectation errors. These are based on judgment biases and emotional biases for investing in companies performing well (Lakonishok, Shieifer, & Vishny, 1994). Thaler has also pushed forward these views with a slightly differing point by noting that there is no evidence to this day that the portfolio of small or value firms can be riskier than the large firms. He also notes that the only thing which makes an economist change his mind in terms of his investment is genuine news. However, there are some other factors that may qualify for humans to react even if these are not news.
6) Figure 11.5 highlights a paper from Rendleman et al. What does this paper suggest to a professional investor? With a similar investor in mind, comment on the conclusion of the Thaler and DeBondt paper (1985); comment on the conclusion of the Banz paper (1981); comment on the conclusion of the Basu paper (1977); and comment on the conclusion of the Arbel paper (1985).
Answer 6
As figure 11.5 shows the cumulative abnormal returns of the stocks after the announcement of the earnings, the paper by Rendleman showed that the stocks’ abnormal returns have a tendency to drift post earnings announcements for several weeks. This is a well-documented anomaly, which is also been studied by hasveral other authors. The earnings surprise can be identified by the earnings which are higher than the estimates of the analysts or higher than the average appreciation of the stock price during the announcement of the earnings. Arbel in 1985 has argued that the stocks which are largely ignored by the analysts should be producing larger returns on average (which implies that these should sell for a lower price) as its investors are facing a larger parameter of the estimation risks (Gervais, Kaniel, & Mingelgrin, 2001). Arbel has referred to these earnings surprises or visibility shocks as “generic stocks”. Basu in 1997 offered convenient and intuitive way of measuring ex-post conservatism, which is based on the observed news. The measure presented by Basu (Patatoukas & Thomas, 2010) captures the difference in the timelines with which the good and bad news were reported in the reflection of the earnings. Banz in 1981 found that the CAPM is missing some factors of reality. He checked whether the firm size is involved in showing the variations in the average returns across different assets, which is not reflected by the beta of the firm. He challenged the CAPM model by concluding that size affects the variations in the mean returns for a specific portfolio of assets. Similarly, in 1987, Thaler and Debont (Bondt & Thaler, 1987) argued that there is a strong likelihood that the high as well as low performing securities in a specific period experience reversal in the preceding years.
7) MIT’s Kindleberger outlines a model to understand the phases of a market bubble. Link the 1996–2000 technology/concept stock bubble to Kindleberger’s framework. Given the model developed by Kindleberger, should one be concerned about today’s equity market here or internationally?
Answer 7
As per Kindleberger, the crisis often follows after a main technical or financial innovation, which presents the investors with new opportunities called the displacements of the expectations of the investors. The lack of familiarity of the investors with the financial and technical innovations can aid in explaining how the investors can overestimate the value of the assets. This is also evident in the example of the dot com companies whose first investors investing in this new class of assets if earned a profit can cause other investors to follow them in investing in innovation, making its price to go higher. This herd behavior of the investors can cause the prices to go way higher than their usual value, which can result in a crash. If the price of the stock falls, then it can result in giving the investors assurance that it is not going to rise again causing them to leave the stock making the price decline. However, the companies which are diversifying into future technologies will grow in terms of their market value because of the reason that their pricing is less risky. The companies who are not innovating and adapting to technological changes are going to suffer the consequences of redundancy and stagnation. The model of Kindleberger is only for the purpose of guiding, which along with the fundamental analysis and sound use of the economic principles can assure the clamping down of the capitalistic overdrive.
8) Kahneman and Tversky (1979) won the Nobel Prize in Economics for their work on prospect theory. Discuss the message of prospect theory. What does their work suggest about what should be the upside and downside market focus of professional money managers? Comment on this in an absolute and a relative return sense.
Answer 8
The Prospect theory suggests that individuals are more focused on gains as compared to losses, and as a result they make decisions that would result in gains. The theory has categorized the risks into two sections. One type of risk is the ones that contribute to gains, the upside risk, and the other ones are the ones that contribute to losses, i.e. the downside risk. As per this theory, people are handling the two risks in entirely different manners to receive a positive gain. In terms of managing portfolio risk, the theory suggests that if investors invest $1000 and then lose 20%, he will then need to make 25% to get back to the starting point. Similarly, if an investor loose 50%, he needs to double to be $1000 again. The theory suggests that people take unnecessary risks to cover their losses, which results in further losses. As per the theory, it is suggested that investors should focus primarily on averting the losses and not on making the gains by managing their downside risks, which would ultimately result in desired growth target (Heukelom, 2015).
9) Explain momentum as a technical tool as well as a factor (see Jegaheesh and Titman, 1993). Discuss the similarities and/or the differences of these two perspectives on momentum. Give an example of a momentum play in today’s marketplace. How is momentum linked, if at all, to the relative strength measure in technical analysis?
Answer 9
The technical momentum analysis MTM is technical analysis indicators that show the difference between the closing price currently trading and the closing price of N days ago. The momentum shows the absolute difference in the stock. On the contrary, the Carhart four-factor models are the extension of the three-factor model of the Fama French which has included the momentum factor for the pricing of the stocks. This is also known as the MOM factor or the monthly momentum factor. The momentum is described as the ability of the price of the stock to continue increasing if it’s going up, and similarly it continues declining if it is going down. The MOM factor is computed by subtracting the equal-weighted mean of the firms who are performing low from the equal-weighted mean of the firms who are performing high, lagged for a month.
The market momentum is the perceived strength of the negative or positive change in the prices of the market. For example, if the index of S&P 500 increases 100 between Tuesday and Monday along with the heavy trading, then it is probably going to remain in an increasing trend in the coming days as well.
The Relative strength index is the measure in which allots stocks a value between 0 and 100. These values are then compared against the other factors like the underbrought or undersold values. The momentum and the RSI both can be used together to show a better timing of the entry and exit points for the investors in the market.
10) Explain why an investor would purchase the premium bond in figure 14.6. In generalized terms, what is the composition of the returns to the premium bond; to a zero-coupon bond; to a bond that is called before maturity?
Answer 10
The investor would buy the premium bond with a 12% coupon rate as its interest rate is higher than that of the normal bond, which means that it is trading at a higher value than the face value of the bond. In terms of the composition of the returns of the bonds, the premium bond higher percentages of the returns arise from the interest payments of the coupon payments. For a zero-coupon bond, all returns come from the capital gains, while in terms of a callable bond, all of the returns come from the coupon or interest payments and the call premium.
11) Arguments arise over the definition of yield-to-maturity. What is the difference, if any, between the yield-to-maturity, the realized yield-to-maturity, and the yield-to-call? Which is always highest?
Answer 11
Yield to Maturity, Yield to Call and Realized Yield to Maturity:
Yield to maturity is the total return that is going to be paid by the bond on its expiration date. It is an important measure for the buyers of the bond. However, the buyers also need to know the yield to call for a bond as well for a callable bond. A callable bond is the one that can redeem before it reaches the date of maturity by its issuer. This is more attractive in terms of its yield to maturity as can be called if there is a change in the interest rates and has the option of borrowing money from other options. The calculation of the yield to maturity is based on the interest payments received from the purchasing date to the maturity date of the bond at the same rate. Thus, it is based on the purchase price, the coupon rate, the face value and the years until maturity. It is computed as;
YTM=(Coupon Rate+(Face Value-(Purchase Price)/(Years until maturity))/((Face value|+Purchase Price)/2)
The yield to call is calculated for a callable bond as the total return, which the investor will receive if the bond is held until its call date and not until full maturity. This bond usually has a higher price than its face value. There are one or more call dates attached to the callable bonds. The YTC is based on the coupon rate of the bond, the time until the first or later date of call, and the market price.
YTC=(Coupon Payment+(Face Value-(Call Price of Bond)/(No of years to call))/((Face value+Call Price of Bond)/2)
The Realized Yield to maturity is the total return for the bond, which is sold before its maturity date. The return can be in the form of interest payments, dividends, or cash distributions. The realized yield is based on the coupon payments received plus or minus the change the value of the investment on annual terms (Scott, 2004).
12) What is the difference between a spot rate, a short rate, and a forward rate? Also, what is the difference between an on-the-run yield curve and a pure yield curve?
Answer 12
Spot rate is the rate of contract, which includes the sale or purchase of the currency and security for immediate delivery with the payment at the spot date. The spot rate is the price of the security or asset at the moment quoted for the spot delivery of the product or currency. On the contrary, the forward contract is the agreement that is made for the price, delivery date, and future specified date. The financial transaction in this contract happens at a future date, and the rate of interest agreed upon is the forward rate for that specific point in time. While, on the other hand, the short rate in the short-term future rate of interest, which is also higher that is charged periodically within a short span of time.
In terms of the yield curve, this curve explains the association between the maturity period of a bond and its yields. This line plots the interest’ rates against time. Examples include the reported yield curves of 2-years, 3-months, 5 years, etc. On the contrary, the pure yield curve is the one that is used for the zero-coupon treasuries. This curve explains the rate of the percentage of the yield to maturity of similar bonds that have differing maturities. The yield curves are lines plotting the interest rates with different maturities.
13) Suppose that an investor observes the following prices and yields to maturity on zero-coupon government bonds: Maturity Price Yield-to-Maturity
1 year 97.50 2.548%
2 years 94.25 2.983
3 years 91.75 2.891
The prices are per 100 of par value; the YTM are stated on a semiannual bond basis.
a) Compute the 1y1y and 2y1y implied forward rates, stated on a semiannual bond basis.
b) The investor has a three-year investment horizon and is choosing between buying the two year zero and reinvesting in another one-year zero in two years or buying and holding to maturity the three-year zero. The investor decides to buy the two-year bond. Based on this decision, what is the minimum YTM the investor expects on one-year zeros two years from now? (3 points)
Answer 13
a-As per the assumption that; 1y1y is the forward rate of 3.419%
A = 2 periods
B = 4 periods
Thus,
B-A = 2 periods
Z2 = 0.02548/2 per period
Z4 = 0.02983/2 per period
Hence,
(1+0.02548/2)^2 x (1+0.02983/2)^4
IFR_2,2=0.017095
x2=0.03419
As per the assumption that; 2y1y is the forward rate of 2.707%
A = 4 periods
B = 6 periods
Thus,
B-A = 2 periods
Z4 = 0.02983/2 per period
Z6 = 0.02891/2 per period
Hence,
(1+0.02983/2)^4 x (1+IFR_4,2 )^2
(1+0.02891/2)^6
IFR_4,2=0.013536
x2=0.02707
b-As the answer is 2.707%, the investors will view the one-year yield in the two years to equal or greater than 2.7%.
Thus, the 2y1y implies that 2.7% is the forward rate, which is also the breakeven investment rate. If the investors are expecting the rate of one year to be less than this in two years, then they would prefer to buy the three years zero instead. Moreover, if the investors are expecting it to be greater than 2.7% then they might prefer the two years zero and then invest the cash flow again.
14) What is figure 16.1 intended to depict? Present in a chart the six rules that Malkiel (1962) and Homer and Liebowitz (1972) articulated in their respective papers.
Answer 14
Figure 16.1 shows the change in the YTM depending on the coupon rates and their Maturity. The four Bonds A, B, C, and D are shown with their changing YTMS. The bonds A and B have 12% coupon rate while their maturity is different and has similar initial YTMs. Bond C and D are shown to have same coupon rate of 3% and same maturity of 30 years with different initial YTMs of 10% and 6%, respectively. In terms of Bonds A and B, the bond with greater maturity i.e. Bond B is witnessing greater change in its bond price with the percentage decline in its YTM as compared to Bond A, who is witnessing a lower change in its price with the change in its YTM. In terms of Bond C and D, the bond with lower initial YTM i.e. Bond D is witnessing a greater change in its bond price with the change in its YTM as compared to Bond C.
The six rules presented by Malkiel, Homer, and Liebowitz in their respective papers are shown below.
- The price of the bond changes inversely with the changes in the interest rates of the market.
- The maturity term and the changes in the prices of the bonds are positively related. Also, for a specific change in the interest rates of the market, the price of the bond changes is higher for the bonds with long-term maturities.
- With the increase in the time remaining of the bond until its maturity, the sensitivity of the bond to the interest rate changes in the market increases in a diminishing trend.
- The following changes in the prices of the bonds after the increase in the interest rates of the market are not symmetrical. This is shown by the example that for a specific maturity, the decline in the interest rate of the market would cause a larger rise in the price of the bond as compared to the decline in the price resulting from the same level of increment in the interest rates of the market.
- The volatility of the bond prices is related to the rate of the coupons. The change in the market interest rate will result in a lower change in the price of the bond if the rate of the coupon is higher.
- The price of the bond in terms of its sensitivity to the change in the yield is oppositely related to the YTM at which the bond is selling at that specific time.
15) A Explain the difference between positive and negative convexity, highlighting the particular nuance of a callable bond. In short, what does formula 16.5 suggest to an investor?
Answer 15
The difference between the negative and positive convexity is that if the duration of a bond increases its yield, then the bond is considered to have negative convexity while the duration and yields of the bonds rise and fall inversely, it is said to have positive convexity. The callable bonds can usually exhibit negative convexity at certain yields and prices. This is because of the incentive of the issuer to call the bond at par, which increases with the decline in the interest rates. As per figure 16.5 the change in the bond yield is if small then as per the convexity term that is multiplied in the equation with (Δ y) 2, which will be very small and not add much to the approximation. As per this figure, by the rule of duration, the linear approximation will be accurate. Therefore, the convexity is more significant when the interest rate changes are large enough.
16) Using a long-term chart of interest rates (for example, looking back 30 years to the early 1980s) as a backdrop, describe your projection-forecast of interest rates over the next 20 years. Use a 20- to 30-year maturity bond as the basis for your argument.
Answer 16
The following is the chart of the federal funds rate. Historically, the trend of the federal funds rate is showing a downward decline. However, from 2006 to 2016, it has remained constant. The trend line is constantly going up for a period and then falling. Currently, the Fed has made decisions about slashing the rate and bringing it down to 1.75%. The Fed has intentions to bring it lower than that in future.
(Trading Economics, 2019)
The current rate of the 30-year Treasury bond as of October 31, 2019, is 2.17%. However, it is expected that if the November 6th, 2019, meeting of the Fed also resulted in a slash down in the funds rate, then the bond rates are also going to decline. The bond market is also lowering its yields, showing a constant fear of the Fed lowering the interest rates. Thus, it is expected that the rate at 30-year Treasury bonds will decline in the next months and in the year to come.
(Macro Trends, 2019)
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