Fall-02 Investments Zvi Wiener tel: History of Interest Rates and Risk Premiums, BKM Ch 5

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

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

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

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

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

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

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

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

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

Zvi WienerBKM Ch 5 slide 11 Geom.Arith.Stan. SeriesMean%Mean%Dev.% Sm Stk Lg Stk LT Gov T-Bills Inflation Annual Holding Period Returns From Figure 6.1 of Text

Zvi WienerBKM Ch 5 slide 12 Risk Real SeriesPremiums%Returns% Sm Stk Lg Stk LT Gov T-Bills Inflation Annual Holding Period Risk Premiums and Real Returns

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 closely follow financial news!

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.

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

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

Zvi WienerBKM Ch 5 slide 17 Chapter 5 Weblinks Returns on various equity indexes can be located here. Returns on various equity indexes can be located here. Returns on various equity indexes can be located here. Current rates on U.S. and international government bonds can be located on this site 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.

Zvi WienerBKM Ch 5 slide 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 site. 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) 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)

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

Zvi WienerBKM Ch 5 slide 20 Main properties

Zvi WienerBKM Ch 5 slide 21 Portfolio of Random Variables

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

Zvi WienerBKM Ch 5 slide 23 Uniform Distribution abab 1

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

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

Zvi WienerBKM Ch 5 slide 26 Normal Distribution

Zvi WienerBKM Ch 5 slide 27 Normal Distribution symmetric around the mean mean = median skewness = 0 kurtosis = 3 linear combination of normal is normal

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.

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!

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.