Module 1 Flashcards
When liquidity is low, what is the impact to the interest rate?
The interest rate increases, to represent the liquidity premium
Since the investor is not easily able to get their cash, there is a premium, increasing the interest rate.
Real risk free rate
+ Inflation premium
=
Nominal risk-free rate
An investors increase in purchasing power is their:
real rate of return
Interest rate adjusted to remove the effects of inflation:
real rate of return
Compensates investors for the increased price sensitivity to changes in interest rates, as maturity is extended
Maturity Premium
An investors equilibrium rate of return is calculated as:
required rate of return =
+ Risk-free rate
+ Inflation Premium
+ Risk premium
Equilibrium rate of return= required rate of return
Risk premium includes: liquidity, default, maturity
Investors require interest on an investment that is calculated as:
required interest rate =
nominal rate
+liquidity premium
+default premium
+maturity premium
(Interest rate formula)
Rate that contains inflation premium
Nominal interest rate
US T-bills are an example of?
Nominal risk-free interest rates
Real risk-free interest rate is a _ rate, that includes:
theoretical rate
includes no expectation of inflation
Interest rates have many different names that include:
discount rates
opportunity cost
required rate of return
cost of capital
The required rate of return on an investment
Equilibrium rate
(nominal required return)
the market rate of return that investors & savers require to get them to willingly lend their funds
Equilibrium rate
Real risk free rate
+ Inflation premium
=
Nominal risk-free rate
The harmonic mean is used to calculate:
- average share cost purchased over time
- average price/unit
The geometric mean is used to calculate:
- investment returns over multiple periods
- compound growth rates
1+sum of %returns to the power of 1/number of periods
The arithemetic mean is used to calculate:
the average returns over a one-period time horizon
Sum all the returns, then divide by the number of periods.
What is the Holding Period Return
What is the arithmetic mean return and how is it calculated?
The arithmetic mean return is the average of periodic returns. On a TI calculator: Sum all the returns, then divide by the number of periods.
What is the geometric mean return and how is it calculated?
he geometric mean return measures the compound annual growth rate over multiple periods. It is calculated as: Enter the returns as growth factors (1 + Return_i), multiply them together, take the nth root (where n is the number of periods), then subtract 1.
What are the trimmed and winsorized means?
The trimmed mean removes a certain percentage of extreme values (e.g., lowest and highest 5%). The winsorized mean replaces extreme values with the nearest values within the central range of the data set.
What is the real risk-free rate?
The real risk-free rate represents the return on an investment with no risk of financial loss and no expectation of inflation. It reflects the time preference for current consumption over future consumption.
What is the Money-Weighted Rate of Return?
What is the Money-Weighted Rate of Return?
What is the Time-Weighted Rate of Return?
The Time-Weighted Rate of Return measures the compound growth rate of $1 over a specified period. It involves dividing the measurement period into sub-periods based on the timing of cash flows and calculating the holding period return for each sub-period, ultimately providing a performance measure independent of cash flows into and out of the portfolio.
Calculate the Money Weighted Rate of Return on the TI Calculator:
Calculate the Time Weighted Rate on Return on the TI Calculator:
Value the portfolio immediately preceding significant additions or withdrawals, i.e., if an investor bought in T0 a share worth 100, at the end of the year, T1, it is worth 130, and received 3 in dividends at the end of the year, the Holding Period Return is (130-100)+3/100. Calculate these for every HPR. Then to calculate the TWRR, open bracket, multiply the (1+HPR1) x (1+HPR2) and take the square root of that according to the number of periods. You then get to the TWRR.
How do you annualise a HPR which may be shorter or longer than one year
What is the general formula for the present value of a future cash flow
How do you calculate continuously compounding return
What is the Gross Return
The total return on a security portfolio before deducting fees
for the management and administration of the investment account
What is the net return
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.
What is the Real Return
nominal return adjusted for inflation.
What is the relationship between the present value and future value
FV = PV(1+r)^-t
What is a zero-coupon bond
A pure discount debt instruments, no coupons received.
How is the price of a 0 coupon bond calculated
PV = Face Value/(1+YTM)^R
When you calculate the PMT for the purposes of determining the FV of a bond, how is this calculated
you determine the HPR payment, i.e., 10% coupon on a 1000 USD bond the PMT is 100
What are perpetual bonds
bonds with no expiration date
how do you determine the PV of a perpetual bond.
PV = Payment/R
What is the difference between an amortising and a fixed coupon bond
The amortising bond pays out a proportion of the principal as well.
How do you determine an annuity payment on the calculator
Set the FV to 0 and solve for PMT
What is a preferred stock
A stock which pays a fixed dividend expressed as a percentage of its par value.
What is the discount rate for equity securities
the rate of return that will induce them to own an equity share.
How do you value preferred stocks
you take the perpetuity formula which is just in this case the dividend per period/the markets required return on the preferred stock
What are DDMs
Dividend Discount Models, a set of three approaches analysts use to value common stock
How do you calculate the PV of a common stock under a DDM if you assume a constant future dividend?
this is the same as you would a preferred stock, Dprice/Kprice where K is the required return
How is the gordon growth model applied assuming a constant dividend growth rate
How do you calculate the present value of a stock by applying the constant growth dividend discount model, aka the gordon Growth Model?
How do you calculate the present value of a stock by applying a DDM when DDM rates are not constant.
You need to determine the present value of each of the dividends, sum that up, and then discount it by the required rate. The Future Value of a dividend in T1 is simply PV + the dividend rate. the PV in T2 is the Dividend Payment in T2 discounted using the constant growth rate model.
How do you compute a forward rate from spot rate?
Remember that the spot rate, for example for two periods, is equal to the spot rate for 1 period + the forward rate for a one year loan made one year from now, or (1+s2)^2 = (1+S1)(1+1Y1Y). Make the calculations.
What is sample variance?
It is a measure of the dispersion of a dataset around its mean, particularly when the dataset is a sample from a larger population.
How is sample variance calculated?
It is calculated as the average of the squared differences (deviations) between each data point in the sample and the sample mean, adjusted by bias by dividing by n-1, where n is the number of observations. The Adjustment ensures that the sample variance is an unbiased estimator of the population variance.
What is the interpretation of sample variance?
It quantifies how spread out the sample data points are around their mean. A higher variance indicates more variability, while a lower variance indicates the data points are closer to the mean
For a dataset which includes 5 annualised total returns, of 30%, 12%, 25%, 20% and 23%, calculate the sample variance.
- Calculate the mean as x = 30+ 12+…./number of jobs
- Compute the deviations from the mean ( 30-22 =8), 12-22 =-10…..
- Square the deviations 8 squared = 64….
- Sum the squared deviations
- Divide by n-1
The sample variance of 44.5% quantifies the average squared deviation of the returns from the mean return. It indicates that, on average, the squared deviations of the returns from the mean are 44.5%
What is the significance of sample variance or standard deviation?
The larger the variance or standard deviation, the greater the variability or risk in the returns of the managers. For investors, high variability may indicate higher risk, while low variability suggests more consistent performance relative to the mean.
Why is sample variance is less intuitive compared to the standard deviation?
Since variance is in squared units (percentage squared in the example), it’s less intuitive to interpret directly.
How can we calculate the standard deviation from the sample variance
You take the square root of the sample variance to arrive at the standard deviation.
What does the standard deviation signify?
It denotes the percentage by which, on average, the individual returns deviate from the mean
