cfa l1 session 1 quants
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CFA L1 Session 1 Quants NotesTRANSCRIPT
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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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