CAPM notes
2
Investor Objectives
2.1. Measuring Investor Returns
We understand that firms should attempt to maximize investor wealth. But, while we now have a strategic goal, we have a little way to go before we can turn it into an action plan. Companies generate uncertain cash flows over very long time horizons; we need a way of turning these risky income streams into equivalent quantities of hard cash. We will do this in two stages. We start with a careful discussion of interest rates, which will enable us precisely to quantify the returns that investors receive on their investments. We then study enough of the Capital Asset Model to understand how much extra return investors demand when they make a risky investment.
We can convert cash today into cash tomorrow by lending it: if I lend $X for a year today at R% then I get
$X + R × X = $X (1 + R)
(2.1)
back at the end of the year. The interest rate R compensates me for two things. First, if inflation is running at I% then for my spending power to remain constant, I need to receive 1 + I in a year for every dollar that I lend today. Second, I require some sort of compensation for delaying for a year the gratification that I get from consuming. This compensation is called the real interest rate, Rre : if I have $1 of spending power today, the real interest rate guarantees me $1 + Rre of spending power in a year. Since as a result of inflation, each $1 of spending power is equivalent to $ (1 + I ) in a year, I receive a total payment of (1 + I ) (1 + Rre ) in one year.
That is:
1 + R = (1 + I ) (1 + Rre ) .
To distinguish it from the “real” interest rate Rre , the interest rate
R is often referred to as the nominal interest rate. Nominal interest
13
14
Chapter 2. Investor Objectives
rates are the ones that are quoted in the financial markets, and real interest rates will seldom concern us.
Similarly, if I am promised cash in the future then I can borrow today, and use the cash to repay the
Investor Objectives
2.1. Measuring Investor Returns
We understand that firms should attempt to maximize investor wealth. But, while we now have a strategic goal, we have a little way to go before we can turn it into an action plan. Companies generate uncertain cash flows over very long time horizons; we need a way of turning these risky income streams into equivalent quantities of hard cash. We will do this in two stages. We start with a careful discussion of interest rates, which will enable us precisely to quantify the returns that investors receive on their investments. We then study enough of the Capital Asset Model to understand how much extra return investors demand when they make a risky investment.
We can convert cash today into cash tomorrow by lending it: if I lend $X for a year today at R% then I get
$X + R × X = $X (1 + R)
(2.1)
back at the end of the year. The interest rate R compensates me for two things. First, if inflation is running at I% then for my spending power to remain constant, I need to receive 1 + I in a year for every dollar that I lend today. Second, I require some sort of compensation for delaying for a year the gratification that I get from consuming. This compensation is called the real interest rate, Rre : if I have $1 of spending power today, the real interest rate guarantees me $1 + Rre of spending power in a year. Since as a result of inflation, each $1 of spending power is equivalent to $ (1 + I ) in a year, I receive a total payment of (1 + I ) (1 + Rre ) in one year.
That is:
1 + R = (1 + I ) (1 + Rre ) .
To distinguish it from the “real” interest rate Rre , the interest rate
R is often referred to as the nominal interest rate. Nominal interest
13
14
Chapter 2. Investor Objectives
rates are the ones that are quoted in the financial markets, and real interest rates will seldom concern us.
Similarly, if I am promised cash in the future then I can borrow today, and use the cash to repay the