# 7-1 Over a Century of Capital Market History in One Easy Lesson â€‹

Three portfolios of U.S. securities:

- A portfolio of Treasure bills. -> U.S. government debt securities maturing in less than one year.
- As safe an investment as you can make. No risk of default exists. Their short maturity means that the prices of these Treasury Bills are relatively stable. It has a pretty certain payoff. However a
*real*rate of return can not be guaranteed. There is still uncertainty about inflation.

- As safe an investment as you can make. No risk of default exists. Their short maturity means that the prices of these Treasury Bills are relatively stable. It has a pretty certain payoff. However a
- A portfolio of U.S. government bonds.
- These longer-term government bonds are assets whose price fluctuate as interest rates vary.
- Interest rate rises -> bond prices fall
- Interest rate falls -> bond prices rise

- These longer-term government bonds are assets whose price fluctuate as interest rates vary.
- A portfolio of U.S. common stocks.
- Investing in common stocks will result in you sharing the ups and downs of the concerning companies.

Investment performance is related to the risk ranking. One dollar invested in 1. Treasury Bills in 1899 would have grown to 74 dollars in 2017. This is just enough to stay on track with inflation. An investment in 2. U.S. government bonds (long-term). Would have gone up to 293 dollars. An investor who invested a dollar in the common stocks of large U.S. firms would have received a total of 47 thousand dollars.

Rate of return reflects both cash receipts, dividends or interest, capital gains or losses.

Treasury bills have average return of 3.8%/year in nominal terms and 0.9% in real terms. Common stocks had a return of 11.5%/year in nominal terms and therefore earned a **risk premium** of 11.5% - 3.8% = 7.7% over the return of Treasury Bills.

## ðŸ“… Arithmetic Averages and Compound Annual Returns â€‹

Let's say a stock is valued at 100$. There is an equal chance that at the end of the year stock will be worth

- 90$ (-10%)
- 110$ (+10%)
- 130$ (+30%)

**Expected return** = (-10 + 10 + 30) / 3 = +10%

PV = expected cash flow / expected rate of return = 110 / 1.10 = 100$

The expected rate of return of 10% is also the opportunity cost of capital for investments that have the same degree of risk.

If you observe the returns of stock over a large number of years. The arithmetic average of the yearly returns is: (-10 + 10 + 30) / 3 = +10%. The arithmetic average of the return correctly measures the opportunity cost of capital for investments with similar risk.

The average **compound annual return** =

This return is less than the opportunity cost of capital. Investors would not want to invest in in such a stock if they can find another investment that will give them a return of 10% for the same risk. The **net present value** would be NPV = -100 + 108.8 / 1.1 = -1.1

*Moral* = if the cost of capital is estimated from historical returns or risk premiums, use arithmetic average, not compound annual rates of return.