History of Interest Rates and Risk Premiums, BKM Ch 5

1. History of Interest Rates and Risk Premiums, BKM Ch 5 Zvi Wiener tel: 02-588-3049 mswiener@mscc.huji.ac.il http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

2. Factors Influencing Rates • Supply • Households • Institutions • Demand • Businesses • Government’s Net Supply and/or Demand • Federal Reserve Actions BKM Ch 5

3. r1 r0 Demand Q0 Q1 Funds Level of Interest Rates Interest Rates Interest Rates Supply Supply r1 r0 Demand Q0 Q1 Funds BKM Ch 5

4. Real vs. Nominal Rates • Fisher effect: Approximation • nominal rate = real rate + inflation premium • R = r + i or r = R - i • Example r = 3%, i = 6% • R = 9% = 3% + 6% or 3% = 9% - 6% • Fisher effect: Exact • r = (R - i) / (1 + i) • 2.83% = (9%-6%) / (1.06) • Empirical Relationship: • Inflation and interest rates move closely together BKM Ch 5

5. Rates of Return: Single Period HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one Inappropriate for complex securities! BKM Ch 5

6. Rates of Return: Single Period Example • Ending Price = 48 • Beginning Price = 40 • Dividend = 2 • HPR = (48 - 40 + 2 )/ (40) = 25% BKM Ch 5

7. Characteristics of Probability Distributions • 1) Mean: most likely value • 2) Variance or standard deviation • 3) Skewness • * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2. BKM Ch 5

8. Normal Distribution s.d. s.d. mean Symmetric distribution BKM Ch 5

9. Measuring Mean: Scenario or Subjective Returns Subjective returns p(s) = probability of a state r(s) = return if a state occurs 1 to s states BKM Ch 5

10. Basic Statistics • Mean Independence • Standard Deviation Conditioning • Variance Joint distribution • Volatility CDF, PDF • Skewness Regression • Correlation Arithmetic, Geometric • Quantile Normal, Student, … BKM Ch 5

11. Annual Holding Period ReturnsFrom Figure 6.1 of Text • Geom. Arith. Stan. • Series Mean% Mean% Dev.% • Sm Stk 12.6 18.8 39.7 • Lg Stk 11.1 13.1 20.2 • LT Gov 5.1 5.4 8.1 • T-Bills 3.8 3.8 3.3 • Inflation 3.1 3.2 4.5 BKM Ch 5

12. Annual Holding Period Risk Premiums and Real Returns • Risk Real • Series Premiums% Returns% • Sm Stk 15.0 15.6 • Lg Stk 9.3 9.9 • LT Gov 1.6 2.2 • T-Bills --- 0.6 • Inflation --- --- BKM Ch 5

13. Home Assignment • Required: • problems 2, 8, 11, 16, 17 (3rd ed). • • problems 2, 8, 11, 14, 15 (5th ed). • • visit http://research.stlouisfed.org/publications/mt • • closely follow financial news! BKM Ch 5

14. Home Assignment • איזה משני האפיקים הבאים רווחי יותר למשקיע: אפיק א': %5 ריבית מחושבת רבע שנתית או אפיק ב': %3.5 ריבית צמודה למדד מחושבת חצי שנתית. שני האפיקים ברמת סיכון זהה. האינפלציה השנתית שהתממשה היתה %1.5. BKM Ch 5

15. Random Variables • Distribution function of a random variable X • F(x) = P(X  x) - the probability of x or less. • If X is discrete then If X is continuous then Note that BKM Ch 5

16. Moments • Mean = Average = Expected value Variance BKM Ch 5

17. Chapter 5 Weblinks • http://www.bloomberg.com/markets/wei.htmlReturns on various equity indexes can be located here. http://app.marketwatch.com/intl/default.aspReturns on various equity indexes can be located here. http://www.quote.com/quotecom/markets/snapshot.aspReturns on various equity indexes can be located here. http://www.bloomberg.com/markets/rates.htmlCurrent rates on U.S. and international government bonds can be located on this site. • http://www.bondmarkets.comThe site above is from the bond market association. General information on a variety of bonds and strategies can be accessed on line at no charge. BKM Ch 5

18. http://www.investinginbonds.comThe site above is from the bond market association. General information on a variety of bonds and strategies can be accessed on line at no charge. Current information on rates is also available on the www.investinginbonds.com site. http://www.stls.frb.org/The site listed above contains current and historical information on a variety of interest rates. Historical data can be downloaded in spreadsheet format and is available through the Federal Reserve Economic Database (FRED) http://www.stls.frb.org/docs/publications/mt/mt.pdfThe site listed above contains current and historical information on a variety of interest rates. Historical data can be downloaded in spreadsheet format and is available through the Federal Reserve Economic Database (FRED) BKM Ch 5

19. Its meaning ... Skewness (non-symmetry) Kurtosis (fat tails) BKM Ch 5

20. Main properties BKM Ch 5

21. Portfolio of Random Variables BKM Ch 5

22. Uniform Distribution • Uniform distribution defined over a range of values axb. BKM Ch 5

23. Uniform Distribution 1 a b BKM Ch 5

24. Normal Distribution • Is defined by its mean and variance. Cumulative is denoted by N(x). BKM Ch 5

25. 66% of events lie between -1 and 1 95% of events lie between -2 and 2 Normal Distribution BKM Ch 5

26. Normal Distribution BKM Ch 5

27. Normal Distribution • symmetric around the mean • mean = median • skewness = 0 • kurtosis = 3 • linear combination of normal is normal 99.99 99.90 99 97.72 97.5 95 90 84.13 50 3.715 3.09 2.326 2.000 1.96 1.645 1.282 1 0 BKM Ch 5

28. Central Limit Theorem • The mean of n independent and identically distributed variables converges to a normal distribution as n increases. BKM Ch 5

29. Lognormal Distribution • The normal distribution is often used for rate of return. • Y is lognormally distributed if X=lnY is normally distributed. No negative values! BKM Ch 5

30. Lognormal Distribution • If r is the expected value of the lognormal variable X, the mean of the associated normal variable is r-0.52. BKM Ch 5