Economics 330

Fall 2001

Lecture 4

I. Return

II. Risk

A. Interest-rate risk

B. Reinvestment risk

III. Indexed Bond

IV. Theory of Asset Demand

Rate of return is the same as return

Issue: how well does a person do by holding a security over a particular time period?

Return can be defined as the payments to the owner plus the change in the value of the financial asset expressed as a fraction of its purchase price

Formula:

That is,

RET = current yield + rate of capital gain

Note: if interest rates increase this will cause the price of the bond to fall. If the decrease in the price of the bond is sufficient this will result in a capital loss and the bond may be a poor investment.

Risk can be defined as the degree of uncertainty associated with the return on an asset relative to alternative assets

Let’s consider two types of risk:

1. Interest-rate risk

This is the risk associated with an asset’s return that is due to changes in the interest rate

A long-term debt instrument has significant interest-rate risk since there is time for the interest rate to vary

This issue is particularly important if the holding period for the asset is less than the asset’s maturity. If interest rates increase this will cause the asset’s price to fall and it is possible that the investor will experience large capital losses.

2. Reinvestment risk

Reinvestment risk occurs when the proceeds from a short-term bond are reinvested and the future interest rate is uncertain.

This problem occurs when the holding period is longer than the maturity for the asset.

If the interest rate rises this will result in the investor __________________

If the interest rate falls this will result in the investor ___________________

Indexed Bonds

An indexed bond is a bond whose interest and principal payments are adjusted for changes in the price level and whose interest rate thus provides a direct measure of the real interest rate.

Example:

Suppose there is a bond with a $1000 face value and a $40 coupon per year. This bond has a maturity of two years.

Consider its present value assuming the interest rate is 4%:

Suppose inflation in the first year is 10%. Then instead of getting $40 you get $40(1.1) = $44

Suppose inflation in the second year is 5%. Then instead of getting $44 you get $44(1.05) = $46.20

And instead of the $1000 you get $1000(1.1)(1.05) = $1155

**Payments are set up so the payments you receive from this asset will have the real purchasing power of the $40, $40, and $1000 in today’s dollars.

**Set up so that without inflation you earn real interest rate of 4%

What’s the drawback of the indexed bond? Tax treatment! With regard to our tax system, the inflation adjusted premium you receive to give you $40 of real purchasing power each year will be taxed as if it is a gain.

We’ve been talking about financial securities, interest rates, risk and return: let’s put this all together in a theory called the Theory of Asset Demand.

An asset is a piece of property that is a store of value

Asset Demand is a function of wealth, expected return, risk, and liquidity.

Wealth is defined as the total resources owned by an individual including all their assets

Expected Return is defined as the return expected over the next period on one asset relative to alternative assets

Risk is defined as the degree of uncertainty associated with the return on one asset relative to alternative assets

Liquidity is defined as the ease and speed with which as asset can be turned into cash relative to alternative assets

Wealth: Assuming all other variables are held constant (ceteris paribus), then wealth is positively related to asset demand. That is, as wealth increases, holding everything else constant, then asset demand also increases.

Wealth Elasticity of Demand

Necessity: Wealth Elasticity is less than 1

Luxury: Wealth Elasticity is greater than 1

Expected Return: As the expected return on one asset relative to alternative assets increase, and holding all other variables constant, the demand for the asset increases. There is a positive relationship between expected return and asset demand.

Example of how to calculate an asset’s expected return:

Risk: As the risk on one asset relative to alternative assets increases, holding all other variables constant, the demand for the asset decreases. There is a negative relationship between risk and asset demand.

Example of how to measure risk:

Comparison of this asset to another asset that shares the same expected return, but that has a smaller range of returns and more predictable returns.

The risk for the second asset is smaller: you expect this since its range of returns is smaller (5 to 15%) versus (0 to 20%) and because the second asset has more predictable returns.

Liquidity: as an asset’s liquidity increases relative to alternative assets, holding everything else constant, the demand for this asset increases. That is, there is a positive relationship between liquidity and asset demand.

Let’s turn now to briefly talk about diversification: Diversification is supposed to reduce risk. This conclusion is highly dependent upon the degree of correlation between the possible assets.

Consider an example with three possible scenarios:

1. An individual can choose to hold only asset #1

2. An individual can choose to hold only asset #2

3. An individual can choose to hold a mix of asset #1 and asset #2

Let’s describe a carefully constructed example:

Suppose Asset 1 earns 10% in a strong economy and 0% in a weak economy

Suppose Asset 2 earns 0% in a strong economy and 10% in a weak economy

And, furthermore, assume the economy is strong 60% of the time and weak 40% of the time.

Consider both the expected return and the risk for each of the three scenarios above.

1. Option 1

2. Option 2

3. Option 3

Diversification will reduce risk is returns on securities do not move perfectly together