Section 4C

Savings Plans and Investments



Last time we were discussing savings plans.

We have touched investments only a bit.

Namely, we considered total and annual return.

That is mainly theory. We will look at some specifics of the investments which exist in real life now. These are
stocks, bonds, and cash investments.

Three basic types of investments: stocks, bonds, and cash

Stock aka equity
gives you a share of ownership in a company. You purchase it, and the only way to get your money back is to sell it. Because stock prices change with time, the sale may give you either gain or loss on your original investment

Three basic types of investments: stocks, bonds, and cash

A bond aka debt
represents a promise of future cash. You usually buy bonds issued by a government or corporation. The issuer pays you simple (not compound) interest and promises to pay back you initial investment plus interest at some later date.

Three basic types of investments: stocks, bonds, and cash

include savings accounts in banks, certificates of deposits (CD), and U.S. Treasury bills. These investments typically earn compound interest.

Consideration of investments:

  • Liquidity
  • Risk
  • Return

As a rule of thumb, the risker an investment is, the bigger return it promises.

Example. Stocks may drop in value. However, they typically yield higher return than absolutely safe federally insured bank accounts and U.S. Treasury bills.

Consideration of investments:

Historical Return by Category

Category Average annual return
Stocks 6.3%
Bonds 2.0%
Cash 0.9%

Consideration of investments, exercise 37, p.234

Suppose your great-great-grandfather invested $300 at the end of 1900 in each of three funds that tracked the averages of stocks, bonds, and cash, respectively. Approximately how much each investment have been worth at the end of 2012?

Solution: The formula to use is the compound interest formula for interest paid once a year:
\(A=P \times(1+APR)^Y\)
\(P=300\), and \(Y=2012-1900=112\), and historical \(APR\).

Consideration of investments, exercise 37, p.234 ... continued

Solution: The formula to use is the compound interest formula for interest paid once a year:
\(A=P \times(1+APR)^Y\)
\(P=300\), and \(Y=2012-1900=112\)
Stocks (APR=0.063): \(300 \times (1+0.063)^{112} = \$ 281,091 \)
Bonds (APR=0.02): \(300 \times (1+0.02)^{112} = \$ 2756 \)
Cash (APR=0.009): \(300 \times (1+0.009)^{112} = \$ 818 \)

The difference is impressive, but what does that reflect?

... Stock prices in 1933 were a bit lower than in 1900...


By its nature, buying stocks, you become a shareholder of a company.

There are thus two ways to make money with stocks.

You may simply sell it, and get capital gain or loss depending whether the price of your stock went up or down

Some companies distribute part of their profits as dividends

While you are a stockholder, you are entitled to receive the dividends according to the number of shares in your possession

Stocks: stock market information

Share price:
last -- current share price
change -- change from the end of the previous day
%change -- percentage change from the end of the previous day
open/high/low -- the share price at opening of the trading day, the highest and the lowest during this day so far
52 week high/low -- the highest and the lowest share price during the past 52 weeks
volume -- the number of shares that have been traded this day

Stocks: stock market information

The company and its shares
market cap -- total stock value of the company
\( \text{market cap} = \text{total number of outstanding shares} \times \text{share price} \)
P/E ratio -- price-to-earnings ratio (P/E)
\( \text{P/E ratio} = \frac{\text{share price}}{\text{earnings per share over the past year}} \)
dividend -- dividend paid per share (past quarter)
dividend yield -- annual yield of the dividend based on the current data
shares outstanding -- total amount of existing shares

Bonds: face value, coupon rate, maturity date.

Face value is the price you pay to the issuer to buy the bond at the time the bond is issued.

Coupon rate is simple interest rate. The issuer pays it yearly.

Maturity date is the date when the issuer promises to repay.

One may sell and buy bonds on the secondary bond market.

The issuer continues to produce bonds, and the coupon rates vary.

Clearly, bonds with the same maturity date and different coupon rates have different prices even if their face values are the same

Bonds: current yield of a bond.

Current yield tells us about the quality of a particular bond, and is calculated by the formula

\( \text{current yield} = \frac{\text{annual interest payment}}{\text{current price of bond}} \)

While the current price of a bond is just a market price, and may be different from its face value, annual interest payment is fixed:

\( \text{annual interest payment} = \text{coupon rate} \times \text{face value} \)