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Real Risk Free Rate?
Is the rate on a single period loan where there is no expected Inflation.
Nominal Risk-Free Rate?
Nominal= Real Risk + Expected Inflation
Interest Rate can be interpreted as 3 things...
Rate of Return for investment in equilibrium
Dicount Rate - Present Value of Future Cash Flows
Opportunity cost of spending today rather than saving for later
3 Risks that a Security Faces
- Liquidity Risk - Risk of receiving less than fair value for an investment if it must be sold quickly
- Default Risk - risk that borrower will not make promised payments
- Maturity Risk - Prices of long term bonds are more volatile than short term bonds. Longer bonds require more risk premium
Required Rate of Return?
Nominal Interest Rate (Real Interest Rate + Inflation Expected) + Liquidity Risk + Default Risk + Maturity Risk
What is EAR?
Effective Annual Rate - Yearly Rate that investors realize due to compounding
EAR= (1+Periodic Rate)^m-1
Periodic Rate = Yearly Rate /# of periods (m)
ual rate compounded Quarterly
How do you convert an annual stated rate to EAR with continuous compounding?
For 6%, (e^.06)-1
Future Value =?
Present Value =?
Difference between Ordinary Annuity and Annuity Due?
Annuity Due pays out at the beg the Term
PV Perpetuity= PMT/I/Y
Net Present Value is the Present Value of all Future Cash Inflows minus Present value of Projects Cash Outflows
NPV = CF/(1+r)^t
Internal Rate of Return is the interest rate that is required to for the PV of costs to equal PV of income rendering the NPV =0
NPV Decision Rule
- Positive NPVs are accepted
- Negative NPVs are Denied
- If mutually exclusive, only one can be chosen, therefore choose higher NPV
IRR Decision Rule
Accept IRR's that are great than firms Required Rate of Return
Reject IRR's that are less than firms required rate of return.
Holding Period Rate =
Percent Change in value of investment over period it is held
HPR = (Ending Value - Begining Value)+Incoming Cash Flow / Begining Value
Which one can you solve using your calculator cash flows, Money-weighted return or time-weighted return?
Time-Weighted Rate of Return Steps, and defintiion
Time weighted rate of return measures compound growth. It is the rate at which 1$ compounds over a specified performanc horizon.
Steps are to 1. Value portfoilio immediatley preceding additions and subtractions. Then for subperiods over the evaluation period document inflows or outlfow.
2. Compute the HPR of the portfolio for each subperiod. .
3. Get the geometric means of the Investment.
Which one is prefered method of permonace measurment , time weighted or moey weighted, and why?
Time-weighted, because it is not affected by timing of cash flows. For example, if you put in a lot of money just before a time of significant good returns, the Money-weighted will give you a significantly higher return compared with time.
Which one is prefered rate of return is preferred if a money manager has complete control over money flows into and out of an account, time weighted or money weighted?
What is the Bank Discount Rate definition? Formula? Negatives of using it?
Bank Discount Rate is the rate at which Treasury Bills are quoted at.
The equation is (D/F)*(360/t).
- D is the difference between face value and the purchase price
- F= Face Value
- T= # of days remaining until maturity
- Negatives are:
- 1. Quoted on a 360 day/year basis
- 2.Does not take into account Compounding
- 3. Yield is based on Face Value, not purchase price.
What is the Holding Period Yield? Formula?
Holding Period Yield is the total yield the ivestor earns between the purchase date and the Maturity date.
Formula is P1-P0+D1/(P1)
- P1 = price received for instrument at maturity
- P0= Initial price of instrument
- D1= Cash Distributions
What is the Effective Annual Yield? Formula?
Effective Annual Yield, is the Yield Return on an investment including compounding over a full year of holding the investment.
Money Market Yield? Formula?
Money Market Yield is equal to the annual holding period yield, assuming a 360 day per year. Makes Tbills comparable to yild quiotes for interest bearing momney market instruments.
Bond Equivalent Yield? Formula?
Bond Equivalent yield comes from fact that yields on US bonds are quoted as twice the semiannual rate, bc coupon interest is paid in two semi ianual payments.
- ((1+Effective Annual Yield)^.5)-1
- Take Semiannual rate x2. Include compounding.
Definition of Descriptive statistic and Inferential Statistic?
Descriptive are used to summarize the important characteristics of large data-sets. Or describe a population
Inferential are used to summarize characteristics of a large data set from a sample.
4 Types of measurment scales?
Nominal Scale - No particlaru order. Each type gets a number
Ordinal - Every observation is grouped into a category.
Interval - Temperature. Does not work as a ratio, or rather that 10 degrees is not double the heat of 20 degrees
Ratio is like money.
Parameter and sample statistic definition.
Paramter is characteristic of a population. Sample Statistic is a characteristic of a sample that is indicative of a population.
Frequencies of occurences. Must be mutually esclusive.
Relative frequency and cumulative frequency
Relative frequency, are the occurences divided by the total. Cumulative is by summing the frequencies starting at a lower interval.
Geometric mean, definition and equation
It is often used when calcualating investment returns over mulptile periods or when measuring compound growht rates.
Forumla is (X1*X2*X3)^1/n\
Geometri mean is always less than or equal to the arithmetic mean, and the difference inreases as the dispersion of occurences increase
Harmonic mean is? Deifnition?
It is used for computations such as average cost of shares purchased over time.
Formula is N/Sum of (1/xi)
Quartile>? Quintile? Decile? Percnetile?
- Quartile - Distribution divided into 4
- Quintile Distribution divided into 5
- Decile - Divided into 10
- Percentile - Divided into 100
Quantile and measures of central tendency known as?
What is equation to get Y percentile with n data points.?
Measures of location
Mean Absolute Deviation definition and formula?
MAD is the average of absolute values of deviations from the arithmetic mean.
Sum of (|xi-mean|+.../N)
Population Variance and Sample Variance Differences.
Sample Variance is divided by N-1. Will overestimate the population Variance so it is closer to the actual population variance.
Chebyshev's Inequality. Definition and formula?
What is minimum percent of any distrubtion that lie within 2 standard deviations of the mean?
States that for any set of observations regardless of shape of distribution, minimum percentage of obersvations that lie within K standard deviations of the mean are atleast 1-(1/K^2) for all K>1.
1-1/2^2= 1-1/4= .75. 75% of observations lie within 2 standard deviations of the mean
What is coefficient of variation? What is Sharpe Ratio?
Coefficient of variation is the relative maount of variability in a distribution relative to a reference point. Equation is CV= Standard Deviation of X/ Average Value of x. Whatever is less, has less relative disperision from the mean and is therfore less risky.
Sharpe Ratio is the Amount of return per unit of risk that is returned.
Equation is (Portfolio Return - Risk Free Return) / Standard Deviation of Portfolio
- Sharpe Ratio Tips
- 1. If negative Sharpe Ratio, the higher the sharpe ratio does not ipmly that better risk adjusted performance. Increasing risk moves a negative Sharpe ratio closer to zero.
2. Sharpe ratio is useful only when standar deviation si appropriate maeasure of risk. In the case of option, with high probability of low return and low probablility of large losses, the standard deviation may be off, and sharpe ratio too high.
Which way is the longer tail for a positivley skewed distribution? What happens to mean median and mode?
Positivley skewed has a longer tail to the right. Mean>Median>Mode
Kurtosis is what? What do you call and what are characteristics of High Kurotsis, Low Kurtosis and Neutral Kurtosis? What is formula? What is excessive Kurtosis?
- Kurtosis is how high the peak of the normal distribution is.
- High Kurtosis is called LeptoKurtic and has fatter tail
- Medium is called Mesokurtic
- Low is called Platykurtic and has thinner tail
Kurtosis Equation is (1/n)* (Sum of (xi-X mean)^4/(s^4))
Neutral is at 3. Excessive is over abolutve value of 1 deviation from 3.
Skewness Equation? Neutral and Excessive?
Kurtosis Equation is (1/n)* (Sum of (xi-X mean)^3/(s^3))
Neutral is at 0. Excessive is over abolutve value of .5 deviation from 0.
Two Defining Properties of Probability
All occurences of any event are between 0 and 1 inclusive.
The probability of occurences that are mutually exclusive and exhaustive summed equal 1
Empirical Probility? Priori probabiliyt? Subjective Probablility?
Empirical is established using past data. Priori is determined using reaosning and inspection. Subjective is based on opionions.
Odds of an flipping a 1 from a dice.
1 to 5.
Formula of probability of A or B=?
Probabliity of A and B=?
- AorB = PA+PB-PAandB
- Aand B= AxB
Covariance Definition and formula and range?
Covariance is the measure of how two stocks move together.
Covariance = Probability x (Ra-Era)*(Rb-Erb)+....
Covariance can move from negative infiti to positive infiniti
Correlation Forumla and definition?
To make covariances easier to interpret, use correlation which is ranged from 1 to negative 1.
Covariance of two assets/ Standard deviations of two assets multiplied
Portfolio Variance of two asset porftolio equation?
Weight^2*(Variance of A)+(weight)^2*Variance of B) +2* Weight of A*Weight of B* Covariance of A and B
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