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CFA Level 1 - Quantitative Methods, Exams of Mathematics

Massachusetts Institute of Technology (MIT)Mathematics

CFA Level 1 - Quantitative Methods. Default Risk - ✔ Risk that a borrower will not make promised payments Liquidity Risk - ✔ Risk of recieving less than fair value for an investment if it must be sold for cash quickly Required Interest Rate on A Security - ✔ = Nominal Interest Rate + Default Risk Premium + Liquidity Premium + Maturity Risk Premium Real Risk Free Rate / Nominal Risk Free Rate - ✔ - Single period interest rate for a completely risk-free security with no inflation added -

Typology: Exams

2021/2022

Available from 01/12/2023

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CFA Level 1 - Quantitative Methods.
Default Risk - ✔ Risk that a borrower will not make promised payments
Liquidity Risk - ✔ Risk of recieving less than fair value for an investment if it must be
sold for cash quickly
Required Interest Rate on A Security - ✔ = Nominal Interest Rate
+ Default Risk Premium
+ Liquidity Premium
+ Maturity Risk Premium
Real Risk Free Rate / Nominal Risk Free Rate - ✔ - Single period interest rate for a
completely risk-free security with no inflation added
- Nominal = Real Risk Free Rate + Expected Inflation Rate
Required Rate of Return - ✔ Required Rate of Return for an investor to willingly invest
Discount Rate - ✔ Used interchangeably with interest rates, especially in use of
discounting cash flows
Opportunity Cost - ✔ The gain that is missed by not investing in a particular investment
Effective Annual Rate - ✔ The actualy rate of interst that is actually being earned after
compounding more than annually
Continuous Compounding - ✔ 1. Multiply rate by time
2. Multiple answer by e (Second LN)
3. Multiply by PV
Present Value of Perpetuity - ✔ Financial instrument that pays a fixed amount of money
at set intervals over an infinite period of time
Present Value of a Projected Perpetuity - ✔ 1. Calculate PV of Perpetuity
2. Find present value of (N -1)
PV of Uneven Cash Flows - ✔ 1. Clear Memory
2. Enter 0 in CF0
3. Enter Cash Flows in Sequence
4. NPV = Discount Rate
5. ComputeT NPV
FV of Uneven Cash Flows - ✔ 1. Calculate the FV of each individual Cash Flow
2: Then add the results together
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CFA Level 1 - Quantitative Methods.

Default Risk - ✔ Risk that a borrower will not make promised payments Liquidity Risk - ✔ Risk of recieving less than fair value for an investment if it must be sold for cash quickly Required Interest Rate on A Security - ✔ = Nominal Interest Rate

  • Default Risk Premium
  • Liquidity Premium
  • Maturity Risk Premium Real Risk Free Rate / Nominal Risk Free Rate - ✔ - Single period interest rate for a completely risk-free security with no inflation added
  • Nominal = Real Risk Free Rate + Expected Inflation Rate Required Rate of Return - ✔ Required Rate of Return for an investor to willingly invest Discount Rate - ✔ Used interchangeably with interest rates, especially in use of discounting cash flows Opportunity Cost - ✔ The gain that is missed by not investing in a particular investment Effective Annual Rate - ✔ The actualy rate of interst that is actually being earned after compounding more than annually Continuous Compounding - ✔ 1. Multiply rate by time
  1. Multiple answer by e (Second LN)
  2. Multiply by PV Present Value of Perpetuity - ✔ Financial instrument that pays a fixed amount of money at set intervals over an infinite period of time Present Value of a Projected Perpetuity - ✔ 1. Calculate PV of Perpetuity
  3. Find present value of (N -1) PV of Uneven Cash Flows - ✔ 1. Clear Memory
  4. Enter 0 in CF
  5. Enter Cash Flows in Sequence
  6. NPV = Discount Rate
  7. ComputeT NPV FV of Uneven Cash Flows - ✔ 1. Calculate the FV of each individual Cash Flow 2: Then add the results together

Calculating the Growth Rate - ✔ Or use TMV calculator

  1. N = Periods, PV = PV, PMT = 0, FV = FV
  2. Compute I/Y Annual Payments (Amortization) - ✔ 1. N = Years, I/Y = Interest, PV = Loan Amount, FV = 0
  3. Compute Payments Calculate Amortization Schedule - ✔ 1. Calculate Loan Payment
  4. Calculate Interest Component (Beginning balance x I/Y)
  5. Calculate Principal component (Payment - Interest Component) 4.The following beginning balance is the first period balance - principal component only. (Interest goes to bank) Cash Flow Additivity Principle - ✔ Present value of any stream of cash flow equals the sum of the present values of the cash flows. Ex: Cash flows of $100 for 4 Years & a $300 payment that occurs in year 3. Calculate the PV of both and add them together. (Use the Unequal Cash flow method.) NPV - ✔ Present Value of expected cash inflows minus the present value of the expected outflows, discounted at the appropriate rate. Use the Calculator (Cash Flow): Set CF0 = 0 (for profit) Set CF0 = Initial negative outflow (for total NPV) IRR - ✔ Discount rate that makes NPV equal to zero Use Calculator (Cash Flows): 1.CF0 = Initial Cash Outlay 2.CF1.....CFn 3.Compute IRR Capital Budgeting - ✔ The allocation of funds to relatively long range projects or investments Capital Structure - ✔ The choice of long-term financial for the investments the company wants to make Working Capital Management - ✔ The management of the company's short-term assets (such as inventory) and short term liabilities (such as money owed to suppliers). NPV Decision Rule - ✔ If the investments NPV is positive - Accept Project If the investments NPV is negative - Decline Project

Ratio Scales - Ranking and qual differences between scale values. Also have true 0. Ex: Money. Population and Samples - ✔ Population - All members of a specfic group Parameter - Descriptive measure of the population Sample - A subset of the population Samples statistic - A quantity computer from or used to describe a sample Frequency Distribution - ✔ Tabular display of data summarizing statistical data by assigning it to an interval. Relative Frequency - Percentage of frequencies within each interval Absolute Frequency - Actual number of frequencies within each interval Cumulative Relative/Absolute Frequencies - Cumulative sum of frequncies Histogram - ✔ Graphical representation of an absolute frequency Frequency Polygon - ✔ The midpoint of eaech interval is plotted on the horizontal axis, and the absolute frequency is plotted on the vertical axis. Measures of Central Tendancy (Means) - ✔ Center or average of a data set Quartiles - Divided into Quarters Quintile - Divided into fifths Decile - Divided into 10ths Percentile - Divided into 100ths Median & Mode - ✔ Median - Midpoint of data set Mode - Value that occurs most often Unimodal - One value that occurs most often Bimodal, Trimodal - Multiple values occur most Mean Absolute Deviation - ✔ 1. Calculate Mean

  1. Ignore negative values in answer Population Variance/Population Standard Deviation - ✔ 1. Calculate Mean
  2. Answer will be in (%)^2 format. Sample Variance/Sample Standard Deviation - ✔

Chebyshev's Inequality - ✔ For any set of observations, the percentage of the observations that lie within "k" standard deviation of the mean is atleast (formula) for all k > 1 Semivariance/Semideviation - ✔ Focuses on downside risk. For Variance:

  1. Calculate sample mean
  2. Use only observations equal or below the mean
  3. Use variance formula to calculate
  4. If Semivariance is less than SD, then the SD overstates risk.
  5. Square Root for Deviation Target Semivariance/Target Standard Deviation - ✔ 1. Identify Target
  6. Use numbers below target
  7. Use Variance Formula, but use total number of observations for N (instead of just the numbers used in formula)
  8. Square Root for Deviation Chebyshev's Inequality (2) - ✔ The following relationships hold for any distribution Coefficient of Variation/Relative Dispersion - ✔ Relative Dispersion - the amount of variability in a distribution relative to a reference point or benchmark CV - Common measurement for relative dispersion Sharpe Ratio - ✔ - Higher the number, the better
  • The extra reward that you recieve for the added risk is called the "Mean excess return" Skewness (Effects on Mean, Median, Mode) - ✔