# ECON 3 Lecture Notes - Lecture 16: Risk-Free Interest Rate, Capital Formation, Risk Premium

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Published on 20 Feb 2016
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Question
When Federal Reserve actions cause interest rates on newly issued bonds to increase from 5%
to 6%, the prices of existing bonds: (Price the day after relative to the price the day before.)
A. Increase
B. Decrease
C. Increase only if the coupon rate is <6%
D. Decrease only if the coupon rate is <6%.
\$1000 face value (principal), coupon rate 7%
Day before:
Price=1070
1.05
=\$1,019
Price=1070
1.06
=\$1,006
The price of the bond will be equal to the face value of the bond when the interest rate is equal
to the coupon rate.
Stocks
Definition: A share of stock (or equity) is a claim to partial ownership of a firm.
2 types of returns to stocks:
Dividends: regular payment for each share of stock. Depends on recent profits.
Capital gains: The increase in price of stocks.
The stock price depends on the supply and demand for a company’s shares. If the company
expects higher future profits, they will increase demand for stock.
Suppose prevailing interest rate on bonds is 5%.
Stock price is expected to be \$75 next year.
Company expects to pay a dividend of \$2/share next year.
How much will you pay for stock now?
Stock price now x 1.05 = \$75 + \$2 = \$77: Must give same yield as bond
Stock price now = \$73
But if stock is riskier than bonds, you will demand a risk premium.
In general, stock price now x (1+risk-free interest rate<- interest rate on US government bonds + risk premium) =
Stock price tomorrow + dividend.
So: an increase in risk free rate leads to decrease in stock price now
an increase in risk premium leads to a decrease in stock price now
an increase in expected dividend leads to an increase in stock price now
an increase in expected future price of stocks leads to an increase in stock price now
You expect a share of Acme Dynamite to sell for \$56 a year from now and to pay a dividend of
\$1 per share annually. If the current interest rates on government bonds is 5%, but you demand
a risk premium of 5% to hold a share of this risky stock, what is the most you should pay for this
stock today (rounded to the nearest dollar)?
z x (1+.05+.05) = 56 + 1
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z x 1.1 = 56 +1
z x 1.1 = 57
z = 57/1.1 = 51.81
2 Important Roles Played by Bond and Stock Markets
1. Information
Any company issuing stocks or bonds is analyzed by Wall Street professionals and others.
Returns will reflect info on risk and future profitability. The search for high returns leads to the
allocation of funds to more productive uses.
2. Risk sharing and diversification
Diversification is the practice of spreading one’s wealth over a variety of different financial
investments in order to decrease overall risk.
Benefits of Diversification
Suppose you have \$200 to invest and you are considering 2 stocks, each of which is selling at
\$100/share.
Increase in Stock Price Per Share
Actual Weather Umbrella Co. Suntan Lotion Co.
Rainy +\$10 Unchanged
Sunny Unchanged +\$10
Suppose the chance of rain is 50% and the chance of sunshine is 50%. How should you invest?
Umbrella: \$200:
2 shares = (0.5 x 20) + (0.5 x 0) = \$10
1 share of each: +\$10 when it’s raining, +\$10 when it’s sunny
A Note on Stock and Bond Exchange
There are millions of shares of stocks and bonds traded daily in US financial markets.
The vast majority represent what is often called the secondary market, which refers to trades
between savers rather than between savers and borrowers.
Since no new funds are allocated from savers to borrowers, no new capital formation is taking
place.
Saving, Investment, and Financial Markets
We will now combine our analysis of saving with our analysis of investment to show the market
for saving and investment.
Investment is the demand for saving.
The price that clears this market is the real interest rate.
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## Document Summary

When federal reserve actions cause interest rates on newly issued bonds to increase from 5% to 6%, the prices of existing bonds: (price the day after relative to the price the day before. ) C: decrease only if the coupon rate is <6%. Increase only if the coupon rate is <6% The price of the bond will be equal to the face value of the bond when the interest rate is equal to the coupon rate. Definition: a share of stock (or equity) is a claim to partial ownership of a firm. Dividends: regular payment for each share of stock. Capital gains: the increase in price of stocks. The stock price depends on the supply and demand for a company"s shares. If the company expects higher future profits, they will increase demand for stock. Suppose prevailing interest rate on bonds is 5%. Stock price is expected to be next year. Company expects to pay a dividend of /share next year.