Rates part 2
- 1. Rates: Interest, Discount & Return Part 2
- 2. “the role of asymptotics in the approximations that many people take as purely formulaic” 2
- 3. Stock Prices • Example: INTC o August 2006 to August 2016 o Monthly price sampling frequency o Adjusted close prices • Adjusts for dividends and splits o Source: Yahoo Finance 3
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- 6. 6 Adjusted close price includes dividends paid out and adjusts for splits Rows must be reversed
- 7. Dividends and Splits 7 Dividend When a stock pays out a dividend, a share loses value equal to the dividend. The total value of the firm’s equity is decreased by the total dividends paid out Pxd = P – d Split In a 2 for 1 stock split, the company doubles the number of shares which cuts the value per share in half. The total value of the firm’s equity does not change
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- 9. Example 9
- 10. Price Summary 10
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- 12. 12 Pi
- 13. 13 ln(Pi)
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- 15. Rates Of Return 15 ri is the simple, total rate of return on stock price, P, from month i-1 to month i ui is the natural log, total rate of return on the log of stock price, ln(P), from month i-1 to month i i is index for months 0 ≤ i ≤ n Pi includes dividends and adjustments for splits for period i and all previous periods
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- 23. Central Limit Theorem • Additive random errors accumulate to a normal distribution o Symmetric o Unimodal o Exponential tails o Mean = mode = median • Multiplicative random errors accumulate to a lognormal distribution o A symmetric with right tail o Unimodal o Exponential tails o Mean > median > mode 23
- 24. Rate of Return • Simple and natural log rates are random variables • Either can be used in price models • How are the rates distributed? o Measure of central tendency • Mode, median, mean o Measure of spread • Standard deviation, variance, range, IQR o Measure of skew o Measure of kurtosis o Distribution • Independent o Implies non-correlation • Identically distributed 24
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- 50. Some useful R commands 50 qqnorm(…) qqline(…) par(mfrow=c( .., ..)) hist(…) curve(dnorm(…), add=TRUE, ... ) kable( ... ) library(e1071) kurtosis() plot(x,y1, … , type=‘l’, ...) lines(x,y2, ... )