Volumne 1- Quantitative Methods Economics

Question 1

Interest Rate (or Yield)

Answer 1

The rate of return that reflects the relationship between differently dated- timed- cash flows.

(CF2-CF1)/CF1 = r

r= Real risk free interest rate+ inflation Premium+ default Risk premium+ Liquidity Premium+ Maturity Premium

Question 2

Three ways we can think of interest rates

Answer 2

Determining the type of interest rate is based on Cash Flows.

1. Required Rate of Return- the minimum rate of return an investor must receive to accept an investment.
2. Discount rates- used when determining the value of a dollar today vs the value of a dollar in the future (used interchangeably with the word interest rates)
3. Opportunity Cost- The value investors forgo by choosing a course of action.

Question 3

Real Risk- Free

Answer 3

The single-period interest rate is for a completely risk-free security if no inflation were expected.

Reflects the time preferences of individuals for current vs real consumption.

Question 4

Inflation Premium

Answer 4

Compensates investors for expected inflation.

The average inflation rate over the maturity of the debt.

Question 5

Default- Risk Premium

Answer 5

Compensation for investors in case the borrower fails to make a payment on time

Question 6

Liquidity Premium

Answer 6

Compensation for the risk of loss relative to investments’ fair value if the cash needs to be converted into cash quickly.

Reflects the relatively high cost associated with selling a position. T bills do not have liquidity premiums due to their volume, but smaller issuers may.

Question 7

Maturity Premium

Answer 7

compensates investors for the increased sensitivity of debt’s market value to changes in market interest rates as maturity is extended, holding all else equal.

The difference between loner term maturity debt and sorter term maturity debt usually reflects a positive maturity premium for longer term debt.

Question 8

Nominal Risk-Free Rate

Answer 8

Real Risk Free Rate+ inflation Premium

(1+nominal risk Free rate) = (1+ Real Risk Free rate)(1+inflation Premium)

Nominal risk-free rate= Real Risk- Free rate+ Inflation Premium

Question 9

Risk-Free Rates

Answer 9

90-day T bill. (quoted in annualized rate of return)

For other countries, bills with maturities of 12 months or less (usually)

Question 10

Two types of returns generated by financial assets

Answer 10

1. Periodic income through dividends or interest Payments
2. Changes in the price of a financial asset

Question 11

Holding Period Return

Answer 11

The return earned from holding an asset for a single specified period (can be any unit of time)

Capital gains is the difference in price between the two periods

the income yield is the income portion

R=((P1-P0 )+I)/P0

Question 12

Arithmetic or Mean rate

Answer 12

• The simplest way to compute average returns
• Best used over a one period horizon as it is the mean average of one period returns
• does not account for the timing of cash flows into and out of portfolios

Ri= (R1+R2+R3+….)/T

Question 13

Geometric Mean or compound rate of return

Answer 13

• best used to estimate returns over more than one time period
• assumes the amount invested at the beginning of each period is the same
• does not account for the timing of cash flows into and out of portfolios
• The previous year’s earnings must be added to the beginning value of the subsequent year.
• The geomean accounts for the compounding of returns.
• more accurate than the arithmetic mean for measuring portfolio growth.
• Geomean is never more than the aritmettic mean

R= root((1+R1)(1+R2)(1+R3)*….) -1

Question 14

Harmonic Mean

Answer 14

• best used in the presence of outliers.
• used most often to average ratios (eg. P/E ratios)
• Special type of weighted mean
• an observations weight in inversely proportional to its magnitude

R= n/sum(1/Xi)

Question 15

Cost Averaging

Answer 15

• The practice of investing a fixed dollar amount on a regular basis regardless of share price.

Question 16

relationship between Arithmetic , Geometric and Harmonic Mean

Answer 16

Arithmetic Mean X Harmonic Mean = Geomean ^2

Question 17

Trimmed mean

Answer 17

• Removes a small defined, percentage of the largest and smallest values from a dataset before calculating the mean by averaging the remaining observations.

Question 18

Winsorized mean

Answer 18

A method of averaging that initially replaces the smallest and latest values with the observations closest to them.

Question 19

Money Weighted Return

Answer 19

• Similar to the internal rate of return and bond YTM
• Accounts for the money invested and provides the investor with the actual rate of return earned on investment.

Question 20

Internal Rate of Return

Answer 20

-The discount rate at which the sum of present values of cash flows will equal zero
- CF can be positive or negative (positive is an inflow to the investor, negative is money flowing away from the investor)
- CF0 is the cash flow at the end of year zero/ beginning of year one

SUM(CF/(1+IRR)^t)=0

Question 21

Time-weighted rate of Return

Answer 21

• measured compounded growth of USD1 initially invested in the portfolio over a statated measurement period
• preferred performance measure of publically traded securities because it neutralizes the effects of cash flows to the portfolio, which are usually out of the control of the manager

Question 22

Three steps to computing time-weighted returns

Answer 22

(1) Price portfolios immediately before any significant addition or withdrawal of funds.
(2) break the overall evaluation period into sub-periods based on the dates of Cash inflows and Outflows.
(3) Calculate the holding period return on the portfolio for each sub-period.
(4) link or compound holding period returns to obtain an annual rate of return for the year. If the investment is for more than one year, take the geometric mean of the annual return for the year to obtain the time-weighted rate of return over that measurement period.