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

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

3. Zvi WienerBKM Ch 5 slide 3 Q0Q0 Q1Q1 r0r0 r1r1 Funds Interest Rates Supply Demand Interest Rates Supply Q0Q0 Q1Q1 r0r0 r1r1 Funds Demand Level of Interest Rates

4. Zvi WienerBKM Ch 5 slide 4 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 Real vs. Nominal Rates

5. Zvi WienerBKM Ch 5 slide 5 HPR = Holding Period Return P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one Inappropriate for complex securities! Rates of Return: Single Period

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

7. Zvi WienerBKM Ch 5 slide 7 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. Characteristics of Probability Distributions

8. Zvi WienerBKM Ch 5 slide 8 Symmetric distribution mean s.d. Normal Distribution

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

10. Zvi WienerBKM Ch 5 slide 10 Basic Statistics MeanIndependence Standard DeviationConditioning VarianceJoint distribution VolatilityCDF, PDF SkewnessRegression CorrelationArithmetic, Geometric QuantileNormal, Student, …

11. Zvi WienerBKM Ch 5 slide 11 Geom.Arith.Stan. SeriesMean%Mean%Dev.% Sm Stk12.618.839.7 Lg Stk11.113.120.2 LT Gov 5.1 5.4 8.1 T-Bills 3.8 3.8 3.3 Inflation 3.1 3.2 4.5 Annual Holding Period Returns From Figure 6.1 of Text

12. Zvi WienerBKM Ch 5 slide 12 Risk Real SeriesPremiums%Returns% Sm Stk 15.015.6 Lg Stk 9.3 9.9 LT Gov 1.6 2.2 T-Bills --- 0.6 Inflation --- --- Annual Holding Period Risk Premiums and Real Returns

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

14. Zvi WienerBKM Ch 5 slide 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.

15. Zvi WienerBKM Ch 5 slide 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

16. Zvi WienerBKM Ch 5 slide 16 Moments Mean = Average = Expected value Variance

17. Zvi WienerBKM Ch 5 slide 17 Chapter 5 Weblinks http://www.bloomberg.com/markets/wei.html http://www.bloomberg.com/markets/wei.html Returns on various equity indexes can be located here. http://app.marketwatch.com/intl/default.asp Returns on various equity indexes can be located here. http://www.quote.com/quotecom/markets/snapshot.asp Returns on various equity indexes can be located here. http://www.bloomberg.com/markets/rates.html Current rates on U.S. and international government bonds can be located on this site. http://app.marketwatch.com/intl/default.asp http://www.quote.com/quotecom/markets/snapshot.asp http://www.bloomberg.com/markets/rates.html http://www.bondmarkets.com http://www.bondmarkets.com The 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.

18. Zvi WienerBKM Ch 5 slide 18 http://www.investinginbonds.com http://www.investinginbonds.com The 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.pdf 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/ http://www.stls.frb.org/docs/publications/mt/mt.pdf

19. Zvi WienerBKM Ch 5 slide 19 Its meaning... Skewness (non-symmetry) Kurtosis (fat tails)

20. Zvi WienerBKM Ch 5 slide 20 Main properties

21. Zvi WienerBKM Ch 5 slide 21 Portfolio of Random Variables

22. Zvi WienerBKM Ch 5 slide 22 Uniform Distribution Uniform distribution defined over a range of values a  x  b.

23. Zvi WienerBKM Ch 5 slide 23 Uniform Distribution abab 1

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

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

26. Zvi WienerBKM Ch 5 slide 26 Normal Distribution

27. Zvi WienerBKM Ch 5 slide 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

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

29. Zvi WienerBKM Ch 5 slide 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!

30. Zvi WienerBKM Ch 5 slide 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.