# Quant Methods

## 39 terms · CFA Level 1 Quant Method Formulas

### Nominal Risk Free Rate

= Real Risk Free Rate + Expected Inflation Rate, Nominal risk free rate = real risk-free rate + expected inflation rate

### Required Interset Rate on a Security

Nominal Risk - Free Rate

### Effective Annual Rate (EAR)

= (1+Periodic Rate)^M-1

e^r-1=EAR

(PMT) / (I/Y)

=PV(1+I/Y)^N

= Sum CF/(1+r)^t

### Bank Discount Yield

= (Discount/Face) * (360/t)

### Holding Period Yield

((P1 + D1) / P0)) -1, (face value - price)/price

where price = purchase price

### Effective Annual Yield

EAY = (1 + HPY)^365/t - 1 where t is days to maturity. Remember that EAY &gt; bank discount yield, for three reasons: (a) yield is based on purchase price, not face value, (b) it is annualized with compound interest (interest on interest), not simple interest, and (c) it is based on a 365-day year rather than 360 days. Be prepared to compare these two measures of yield and use these three reasons to explain why EAY is preferable.

### Money Market Yield

= HPY * (360/days until maturity)

μ = ( Σ Xi ) / N

### Sample Mean

x̄ = ( Σ xi ) / n

### Geometric Mean Return

1+ Geo mean return =
((1+Return 1) (1+Return 2) (1+Return n)) ^ 1/n

Where 'n' represents the number of returns in the series.

The geometric mean must be used when working with percentages (which are derived from values), whereas the standard arithmetic mean will work with the values themselves.

The main benefit to using the geometric mean is that the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an "apples-to-apples" comparison when looking at two investment options.

=N/ (SUM 1/Xi)

### Position of the Observation at a Given Percentile

= (n+1) * (y/100)

### Range

Max Value - Min Value

### Excess Kurtosis

= Sample Kurtosis - 3

The mean distance of the data from the mean. (Sigma (absval: x - xbar))/n

### Population Variance

σ² = Σ ( Xi - μ )² / N

Where μ = Population Mean and N = Number of possible outcomes

### Sample Variance

s²=∑(x-x̄)²/n-1

Where x̄ = Sample Mean and n = Sample Size

### Coefficient of Variation

= s / x̄

Standard Deviation of Sample divided by Sample Mean

### Sharpe Ratio

(Rp - Rf) / σp

excess returns per unit of total portfolio risk, higher ratio indicate better risk-adjusted portfolio performance. Uses total risk rather than systematic.

### Joint Probability

P(AB) = P(A|B) * P(B)
P(A|B) = P(AB)/P(B)

P(A or B) = P(A) + P(B) - P(A and B)

### Multiplication Rule

if events A and B are independent, then P(A and B) = P(A)*P(B)

### Total Probability Rule

-Unconditional Probability of an event , given conditional probabilities

P(A) = P(A | B1) P(B1) + P(A | B2) P(B2) + ... + P(A | BN) * P(BN)

Assumes B1 - BN are mutually exclusive.

E(X) = ∑P(xi)xi

### Covariance

= [(R(x)-ER(x)]*[R(y)-ER(y)]

### Correlation

= Cov(Rx,Ry)/ (Stdv X * Stdv Y)

### Portfolio Variance

= (Wa²)(σa²) + (Wb²)(σb²) + 2(Wa)(Wb)(COV a,b)

### Combination Binomial Formula

aCr = n! / (n-r)!

### Binomial Probability

p(x) = [n!/(n-x)!x!]*[P^x(1-p)^(n-x)]

### 90% Confidence Interval

x̄ - 1.65s to x̄ + 1.65s

### 95% Confidence Interval

x̄ - 1.96s to x̄ + 1.96s

### 99% Confidence Interval

x̄ - 2.58s to x̄ + 2.58s

### Semi Variance

The average of squared deviations that fall below the mean
(downside risk measure)

(∑|x-xbar|)/n

### Probability of x succeses in n trials

(n! / ((n-x)!x!))p(1-p)^n-x