1 Rates and Return

The continuously compounded rate of return that will generate a one-year holding period return of -6.5% is closest to:

-6.7%. Continuously compounded rate of return = ln(1 - 0.065) = -6.72%.

Vega research has been conducting investor polls for Third State Bank. They have found the most investors are not willing to tie up their money in a 1-year (2-year) CD unless they receive at least 1.0% (1.5%) more than they would on an ordinary savings account. If the savings account rate is 3%, and the bank wants to raise funds with 2-year CDs, the yield must be at least:

4.5%, and this represents a required rate of return. Since we are taking the view of the minimum amount required to induce investors to lend funds to the bank, this is best described as a required rate of return. Based upon the numerical information, the rate must be 4.5% (= 3.0 + 1.5).

Trimmed or winsorized mean

Decrease the effect of outliers

Which of the following return measures is best described as purely representing time preference?

Real risk-free interest rate. The real risk-free interest rate represents time preference, or the degree to which consumers prefer consumption in the present to an equal amount of consumption in the future. Other measures of return include time preference, but it also reflect other factors, such as risk or expected inflation.

Liquidity risk

This is the risk of receiving less than fair value for an investment if it must be sold quickly for cash.

Default risk

This is the risk that a borrower will not make the promised payments in a timely manner

Two of the methods for dealing with outliers are

a trimmed mean and a winsorized mean

real rate of return

an investor's increase in purchasing power (after adjusting for inflation). Because expected inflation in future periods is not zero

Interest rates and market returns are typically stated as

annualized returns

money-weighted return

applies the concept of the internal rate of return (IRR) to investment portfolios

The only time the arithmetic and geometric means

are equal is when there is no variability in the observations (i.e., all observations are equal).

Selmer Jones has just inherited some money and wants to set some of it aside for a vacation in Hawaii one year from today. His bank will pay him 5% interest on any funds he deposits. In order to determine how much of the money must be set aside and held for the trip, he should use the 5% as a:

discount rate. He needs to figure out how much the trip will cost in one year, and use the 5% as a discount rate to convert the future cost to a present value. Thus, in this context the rate is best viewed as a discount rate.

Interest rates are also referred to as

discount rates

An investor with a buy-and-hold strategy who makes quarterly deposits into an account should most appropriately evaluate portfolio performance using the portfolio's:

geometric mean return. Geometric mean return (time-weighted return) is the most appropriate method for performance measurement as it does not consider additions to or withdrawals from the account.

For a given stated annual rate of return, compared to the effective rate of return with discrete compounding, the effective rate of return with continuous compounding will be:

higher. A higher frequency of compounding leads to a higher effective rate of return. The effective rate of return with continuous compounding will, therefore, be greater than any effective rate of return with discrete compounding.

geometric mean return

is a compound rate. When periodic rates of return vary from period to period, the geometric mean return will have a value less than the arithmetic mean return:

money-weighted rate of return

is defined as the IRR on a portfolio, taking into account all cash inflows and outflows. The beginning value of the account is an inflow, as are all deposits into the account. All withdrawals from the account are outflows, as is the ending value.

Real return

is nominal return adjusted for inflation

Holding period return (HPR)

is simply the percentage increase in the value of an investment over a given period:

IRR

is the interest rate at which a series of cash inflows and outflows sum to zero when discounted to their present value

arithmetic mean return

is the simple average of a series of periodic returns. It has the statistical property of being an unbiased estimator of the true mean of the underlying distribution of returns

harmonic mean

is used for certain computations, such as the average cost of shares purchased over time

If funds are contributed to an investment portfolio just before a period of relatively poor portfolio performance, the money-weighted rate of return will tend to be

lower than the time-weighted rate of return

Interest rates

measure the time value of money, although risk differences in financial securities lead to differences in their equilibrium interest rates.

Time-weighted rate of return

measures compound growth and is the rate at which $1 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time.

Real return

measures the increase in an investor's purchasing power—how much more goods she can purchase at the end of one year due to the increase in the value of her investments.

real risk-free rate

of interest is a theoretical rate on a single-period loan that contains no expectation of inflation and zero probability of default.

we can also view interest rates as the

opportunity cost of current consumption

Wei Zhang has funds on deposit with Iron Range bank. The funds are currently earning 6% interest. If he withdraws $15,000 to purchase an automobile, the 6% interest rate can be best thought of as a(n):

opportunity cost. Since Wei will be foregoing interest on the withdrawn funds, the 6% interest can be best characterized as an opportunity cost — the return he could earn by postponing his auto purchase until the future.

In the investment management industry, time-weighted return is the

preferred method of performance measurement because portfolio managers typically do not control the timing of deposits to and withdrawals from the accounts they manage.

leveraged return

refers to a return to an investor that is a multiple of the return on the underlying asset. The leveraged return is calculated as the gain or loss on the investment as a percentage of an investor's cash investment.

After-tax nominal return

refers to the return after the tax liability is deducted.

Net return

refers to the return after these fees have been deducted. Commissions on trades and other costs that are necessary to generate the investment returns are deducted in both gross and net return measures

Pretax nominal return

refers to the return before paying taxes. Dividend income, interest income, short-term capital gains, and long-term capital gains may all be taxed at different rates

Gross return

refers to the total return on a security portfolio before deducting fees for the management and administration of the investment account.

What the real risk-free rate represents in economic terms is time preference

the degree to which current consumption is preferred to equal future consumption.

if funds are contributed to a portfolio at a favorable time (just before a period of relatively high returns),

the money-weighted rate of return will be higher than the time-weighted rate of return.

Maturity risk

the prices of longer-term bonds are more volatile than those of shorter-term bonds. Longer-maturity bonds have more maturity risk than shorter-term bonds and require a maturity risk premium.

time-weighted rate of return is not affected by

the timing of cash inflows and outflows