distribution of outcomes either historically or projecting into the future

# Distribution of outcomes either historically or

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distribution of outcomes (either historically or projecting into the future) follows a normal (or, “bell curve”) distribution In reality, investment (such as stock) returns over time may follow a skewed distribution – a distorted version of the normal bell curve In this class, though, we’ll stay with the assumption of “normality” FIN 300 - Risk and Return Pt. 1 29
Normal Distribution Graphs Approximately 68% of the time, the return is expected to be within +/- 1 standard deviation ( ) of the mean Roughly speaking, 2/3 of the time you are within +/- 1  of the mean 1/3 of the time, you are in the tails (either at points less than 1  below the mean – or greater than 1  above the mean) As investors, we lose sleep over the bad outcomes (in the “left tail”) Due to the symmetry in the bell-curve, 1/6 of the time, we expect to have a worse outcome than that 1 below the mean FIN 300 - Risk and Return Pt. 1 30
Normal Distribution FIN 300 - Risk and Return Pt. 1 31
Normal Distribution Example: S&P 500 Stock Index 80+ year historical data Mean annual return is roughly 10% Annual returns have a standard deviation of roughly 20% Based on the long-term historical stats, the annual return would be worse than -10% in 1 of every 6 years 1/6 of the time, expect to lose 10% of your investment! This is not an unusual event – stocks are risky FIN 300 - Risk and Return Pt. 1 32
Normal Distribution FIN 300 - Risk and Return Pt. 1 33 S&P 500 Index: Mean = 10% 1/6 of the time >  1/6 of the time <  S&P 500 Index: 
Historical Investment Data Let’s look at some charts illustrating historical returns for different asset classes Examples of “asset classes” Large-cap (large market value) stocks – S&P 500 Index Small-cap stocks Short-term U.S. Gov’t securities – such as T-Bills Intermediate-term and longer-term U.S. gov’t securities – T-Notes & T-Bonds Corporate bonds FIN 300 - Risk and Return Pt. 1 34
History of Annual Returns for U.S. Stocks & Bonds FIN 300 - Risk & Return 35
Cumulative Value of \$1 Invested in 1926 Exhibit 7.5 FIN 300 - Risk & Return 36
Historical U.S. Stock Returns (1826! -2008) Source:
Historical Risk & Return – Key Takeaways! Based on long-term averages, we can generally observe the following: Stocks offer a higher return than bonds Accordingly, stocks have more risk than bonds Small-cap (or, “small”) stocks offer a higher return than large-cap (or, “large”) stocks Accordingly, small stocks are risker than large stocks Long-term bonds offer a higher return than short- term bonds Accordingly, long-term bonds are risker than short-term bonds (we saw this, of course, in Chapter 8) FIN 300 - Risk and Return Pt. 1 38
Choosing Among Investments Given: Stock A has a return of 20% and a standard deviation (of returns) of 40% Stock B has a return of 20% and a standard deviation (of returns) of 45% Stock C has a return of 25% and a standard deviation (of returns) of 40% Which one do I choose?

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• Fall '08
• Olander