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Agenda

Quants – Session 1 Dated 15th June 2014

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Time Value of Money (TVM)Interest on Interest • Compounded annually vs semi-annually• Example for demonstration

PV vs FV • Elementary school problem• Use of Financial calculator

Time-lines• Important throughout CFA curriculum• Useful to put things in perspective (pictorial depiction of entire data)• Cash outflow (-ve), cash inflow (+ve)• Discounting vs Compounding• End of the year = Beginning of the next year

Interest rates• Discount factor and its relevance• Nominal risk free rate = real Risk free rate + expected Inflation rate• Required rate of return = Nominal + default risk prem + Liquidity Prem

+ maturity risk prem

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Time Value of Money (TVM)Effective annual rate (EAR)• DO-NOT memorize the formula

Solving TVM for different compounding rate • Option 1 – Calculate EAR• Option 2 – Use periodic rate• Same can be applied for PV as well

Annuity• Ordinary Annuity

• Use of financial calculator• Annuity payments and Interest

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Time Value of Money (TVM)Ordinary Annuity – Starting late

Annuity Due• Change the settings of the calculator

• 2nd -> BGN -> 2nd -> SET-> 2nd -> Quit (RISKY)• PV/FV [AD] = PV/FV [AO] * (1+R) (Understand, & then memorize)

Perpetuity• PVperpetuity = PMT / R

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Time Value of Money (TVM)PV and FV of uneven cash flows

• Rate of interest = 10% • Calculate FV at the end of the sixth year

• How to use calculator the above problem?

Different Compounding periods and the use of Financial Calculator• Adjusting I/Y = (R/m), and n = t*m, where m is the number of periods in a

year

Use of timelines• Loan Amortization

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Time Value of Money (TVM)Use of timelines• Loan Amortization

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Time Value of Money (TVM)TOUGH PROBLEMS

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Discounted Cash Flow ApplicationsNPV – Net Present Value• Accept projects with positive NPV

• Reject the ones with negative NPV• If one of the two mutually exclusive projects needs to be selected –

choose the one with higher NPV

IRR – Internal rate of return

• Accept projects with IRR > firm’s required rate of return• Reject with IRR < firm’s required rate of return

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Discounted Cash Flow ApplicationsConflicts between IRR and NPV

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Discounted Cash Flow ApplicationsHolding Period Return (HPR)

• HPR = (Ending Value – Beginning Value) / Beginning Value• HPR = (Ending Value + Cash Flow – Beginning Value) / Beginning Value

Money-weighted rate of return

Time-weighted rate of return

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Discounted Cash Flow ApplicationsBank Discount Yield

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Discounted Cash Flow ApplicationsHolding Period Yield (HPY)

Effective Annual Yield (EAY)

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Discounted Cash Flow ApplicationsMoney Market Yield (MMY)

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Discounted Cash Flow ApplicationsBond Equivalent YieldBEY = 2 * Semi-Annual Discount Rate

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Statistical Concepts and Market ReturnsDescriptive Statistics• Making sense of a large chunk of dataInferential Statistics• Forecasts about a larger set of data by analyzing a subsetScales of measurement• Nominal scales• Ordinal scales• Interval scales – Assurance that difference b/w two equal intervals is

same• Interval scales based ratios are meaningless

• Ratio scales

• Order of precision• Nominal, Ordinal, Interval, Ratio (NOIR)

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Statistical Concepts and Market ReturnsTerminology of Measurement• Parameter• Sample statistic• Standard deviation of returns• Frequency distribution

• Define Intervals (mutually exclusive)• Tally the observation• Count the observation

• Relative frequency• Cumulative frequency• Histogram – Graphical representation of absolute frequency distribution• Frequency Polygon – Mid point of each interval plotted on x-axis

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Statistical Concepts and Market ReturnsTerminology of Measurement• Population Mean• Sample Mean

• Arithmetic mean is the only measure of central tendency such that the sum of deviations from the mean is “ZERO” – Lets prove it!

• Weighted Mean

• Median• Arrange in ascending or descending order (CRITICAL)• For even number of data = (0.5 * (n/2+(n/2+1))• For odd = (n+1)/2

• Mode – Not necessary to have• Uni-modal, Bi-modal, Tri-modal

Note difference b/w N and n

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Statistical Concepts and Market ReturnsTerminology of Measurement• Geometric Mean

• Note : For returns add 1 to the above formula

• Harmonic Mean

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Statistical Concepts and Market Returns

Remember:

AM>GM>HM

Equality holds if all numbers are equal

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Statistical Concepts and Market Returns

NOTE: Arranging in ascending order is critical

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Statistical Concepts and Market ReturnsDispersion• Variability around the central tendency• Measure of risk (an average perfomer Vs flamboyant performer)

• Range• Max –Min

• Mean Absolute Deviation (MAD)

• Population Variance

• Standard Deviation

• Sample Variance

NOTE:

1) N vs n-1 (unbiased

estimator) vs biased estimator

2) X (bar) vs Mu

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Statistical Concepts and Market ReturnsChebyshev’s Inequality – Spelling is not critical, better formula is• Variability around the central tendency

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Statistical Concepts and Market ReturnsCoefficient of Variation (CV)• Variation alone might not be comparable

Sharpe Ratio – Excess return per unit of risk

• Higher sharpe ratio is preferred• For negative values, the above is not true

Skewness• Symmetrical or not

• Probability of higher gains or losses?• Postively skewed (right tail) vs Negatively skewed (left tail)

• For perfectly skewed• Mean = Median = Mode

• For positively skewed : Mean > Median > Mode• For –vely skewed : Mean < Median < Mode

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Statistical Concepts and Market ReturnsArithmetic Mean vs Geometric Mean

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Statistical Concepts and Market ReturnsKurtosis• Leptokurtic - More• Platykurtic - Less• Mesokurtic - same

Excess Kurtosis = sample kurtosis - 3

+ve for right skewed

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Probability ConceptsTerminologies• Random Variable• Outcome• Event• Mutually exclusive events• Exhaustive Events

0<= P(E) <= 1

Probability of mutually exclusive and exhaustive events add up to 1

Objective Probability vs Subjective ProbabilityEmpirical and A Priori probability – Objective Probability

If probability of an event occurring is 1/8 what are the odds of the event occuring vs the odds against it? – vice-versa

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Probability ConceptsConditional vs Unconditional Probability• Conditional Probability (P (A|B)• Unconditional Probability

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Probability ConceptsAddition Rule of Probability

Independent Events

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Probability ConceptsTotal Probability Rule

Expected Value

Questions:a) What is the expected value in the throw of a dice?b) What is the expected value in a flip of a coin?

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Probability ConceptsVariance

Two step1) Calculate the expected value2) Use the variance formulae

Co Variance and its Properties

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Probability ConceptsExample – Co Variance

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Probability ConceptsExample – Co Variance

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Probability ConceptsExpected return of a portfolio

Variance of a Portfolio

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Probability ConceptsBaye’s Formula – Lets not memorize, lets understand

EXAMPLE:

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Probability ConceptsLabeling – Not very finance specific, but important for the course

EXAMPLE 1:

Permutation and Combination – This is the end, my friend!

• nCr (order is not relevant) and nPr (order is relevant)

EXAMPLE 2:

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