Measuring Return

Question 1

Describe Holding Period Return:

Answer 1

• Holding Period Return = Selling Price - Purchase Price +/- cash flows / Purchase Price or Equity Invested, p 49
  
  • EXAM TIP: Memorize formula, not provided on the exam; possible HPR questions may come from margin returns or after-tax RORs
    
    • Dividends received - add to numerator
    • Margin Interest Paid - Subtract from numerator
    • Taxes paid - only do this if question asks for after-tax gain or loss; subtract from numerator
    • Purchased securities on margin - cost of securities in numerator, equity in the trade goes in the denominator

Question 2

What is the method of calculating Holding Period Return (HPR) when provided with periodic returns (instead of cash flows)?

Answer 2

• HPR=[(1+r₁)x(1+r₂)x…(1+r_n)]-1
  
  • r= % return per period
  • n = number of periods
  • on formula sheet

Question 3

Describe Effective Annual Rate:

Answer 3

• EAR
• calculates the effective annual interest rate earned on an investment when the compounding occurs more often than once per year (e.g. quarterly).
  
  • EAR = (1 + i/n)ⁿ - 1
    
    • i = stated annual interest rate
    • n = number of compounding periods

Question 4

Describe Arithmetic Average:

Answer 4

• Sum of all numbers divided by the number of observations
• AKA: simple average
  
  • on exam sheet
  • AM=a₁+a₂+…+a_n / n
• may give misleading result as it ignores the compounding effect of returns over time

Question 5

Describe Geometric Average:

Answer 5

• Standard formula for finding the geometric mean for a set of observations
  
  • may represent a set of given stock prices over a period of time
    
    • may not be appropriate when calculating geometric mean return given a time series of asset returns because of the possibility of earning a negative or zero return, and because of the compounding. A negative value under the radical makes the formula unusable, as we cannot take the nth root of a neative number, a zero return also causes issues
    • p53
  • Time-wieghted compounded ROR
  • Simply stated, the geometric average is the compounded ROR

Question 6

Describe Weighted Average?

Answer 6

• can be used to calculate a weighted average share price, expected returns, beta or duration
• Process is the same regardless of what is being calculated
• Formula:
  
  • p55

Question 7

Describe Net Present Value:

Answer 7

• Used to evaluate capital expenditures that will result in different cash flows over the useful life or investment period
• NPV is deterministic
  
  • Positive = make the investment
  • Negative = do not make the investment
  • EXAM TIP: if NPV = 0, then YES make the investment
• Formula:
  
  • NPV = PV of Cash Flows - Initial Cost

Question 8

What is Internal Rate of Return (IRR)?

Answer 8

• the discount rate that sets the NPV formula equal to zero
  
  • NPV = PV of Cash Flows - Initial cost
• can also be thought of as compounded ROR
• Should be calculated when you have uneven cash flows and you are asked to calculate a compounded ROR
  
  • If NPV is positive, then IRR > Discount Rate
  • If NPV is zero, then IRR = Discount Rte
  • If NPV is negative, then IRR < Discount Rate

Question 9

• Q1: What is Dollar-Weighted Return?
• Q2: What is Time-weighted Return?

Answer 9

• A1: Calculates IRR using the investor’s cash flows
• A2:
  
  • Calculates IRR using the securities cash flow, assumes buy and hold
  • determined without regard to investor’s cash flows
  • EXAM TIP: Mutual funds report on a TWR basis

Question 10

What is Arbitrage Pricing Theory (APT)?

Answer 10

• Assets that pricing imbalances cannot exist for any significant period of time; otherwise investors will exploit price imbalance until the market prices are back to equilibrium
• APT is a multi-factor moedel that attempts to explain return based on factors.
  
  • Anytime a factor has a value of zero, no impact on return
• APT attempts to take advantage of pricing imbalances
• Inputs:
  
  • Factors: Inflation, risk premium, and expected returns and their sensitivity (b) to those factors
  • Standard deviation and beta are not inputs variables to the APT
• EXAM TIP: don’t memorize formula, but memorize keywords: multi-factor model, sensitivity to those factors, and STD and Beta are not inputs

Question 11

Descrie Foreign Currency Translation:

Answer 11

• Purchase of assets in foreign currency have returns affected by the growth of the security and the relative growth of the foreign currency and the U.S. dollar
  
  • Steps:
    
    • Convert US dollars to the foreign currency to determine cost
    • Compute the return, typically utilizing the holding period calculation
    • Convert foreign currency back to US dollars