Do bonds reduce the overall risk of an investment portfolio Let x b.pdf

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Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data x: 11 0 36 21 31 23 24 -11 -11 -21 y: 10 -2 29 14 22 18 14 -2 -3 -10 (a) Compute ?x, ?x2, ?y, ?y2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds. Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data Compute ?x, ?x2, ?y, ?y2 Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds. Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If s represents risks and represents expected return, then can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain. Solution stop being so complicated: 1) if interest rates rise, you are screwed. interest rates are zero now. nowhere to go but up. 2) if bondholders default, you are screwed. more bankruptcy now than you can shake a stick at. bottom line: bonds have lotsa risk. buy cans of beans and bury them in your backyard..

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PAGE 1 Chapter 5: Normal Probability Distributions Section 5.1: Intro to Normal Distributions and the Standard Normal Distributions Objectives:  Normal Distribution Properties  Use z-scores to Calculate Area Under the Standard Normal Curve (using StatCrunch or Calculator)  Discuss Unusual Values In this section we will revisit histograms which can be estimated with normal (symmetric, bell-shaped) curves. From Test 1 remember that normal curves have z-scores (for any data value) and areas under the curve (one way: Empirical Rule). Now we will use these normal curves to find probabilities (areas) and z-scores for any data value. Why do we need to study this? Eventually we will use these probabilities and z-scores to make decisions. By using the normal distribution curve, we are treating the data as a continuous random variable that has its own continuous probability distribution. (Remember that any probability distribution has two properties: all probabilities are between 0 and 1 and the sum of the probabilities is 1.) **Probabilities = Areas under the curve** Ex: Consider the normal distribution curves below. Which normal curve has the greatest mean? Which normal curve has the greatest standard deviation? Note: Every normal distribution can be transformed into the Standard Normal Distribution (the distribution for z- scores). This means we will use the z-score formula to transform any data value into a “measure of position” with the formula: data value mean standard deviation z   PAGE 2 **All probability calculations will be done with either StatCrunch or the TI 83/84 calculator. You do NOT need to learn how to read the Standard Normal Table.** **Also < and  are treated the same as well as > and  for any continuous probability distribution.** Ex: Confirm that the area to the left of z = 1.15 is 0.8749. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, enter inequality symbol and z-score, Compute TI-83/84: 2nd  VARS normalcdf( -1000000000  Comma  1.15 Comma  0  Comma 1 enter P(z  1.15) = 0.8749 Ex: Confirm that the cumulative area that corresponds to z = -0.24 is 0.4052. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, Standard, enter inequality symbol and z-score, Compute TI-83/84: 2nd  VARS normalcdf( -1000000000  Comma  -0.24 Comma 0  Comma 1 enter P(z  -0.24) = 0.4052 PAGE 3 Ex: Find the area to right of each z-score. Hint: Use the fact that the total area (probability) is 1. **Label the z-score and the area.** a) b) P(z  1.15) = _________________ P(z  -0.24) = _________________ Ex: Find the shaded area. **Label the z-score and the area.** StatCrunch: Stat menu, Calculators, Normal, Stand.

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Commonality in idiosyncratic volatility cannot be completely explained by time-varying volatility. After removing the effects of time-varying volatility, idiosyncratic volatility innovations are still positively correlated. This result suggests correlated volatility shocks contribute to the comovement in idiosyncratic volatility. Motivated by this fact, we propose the Dynamic Factor Correlation (DFC) model, which fits the data well and captures the cross-sectional correlations in idiosyncratic volatility innovations. We decompose the common factor in idiosyncratic volatility (CIV) of Herskovic et al. (2016) into the volatility innovation factor (VIN) and time-varying volatility factor (TVV). Whereas VIN is associated with strong variation in average returns, TVV is only weakly priced in the cross section A strategy that takes a long position in the portfolio with the lowest VIN and TVV betas, and a short position in the portfolio with the highest VIN and TVV betas earns average returns of 8.0% per year.

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