Measuring Return (L3)

Question 1

Holding Period Return (HPR) Memorize Formula

Answer 1

• HPR = (Selling Price - Purchase Price +/- Cash Flows) / Purchase Price OR Equity Invested
• HPR (when provided with period returns)
  ○ Formula provided in CFP Formula Sheet
  ○ HPR = [(1+r1) (1+r2) …(1+rn)] -1
  ———————————————————————————–
• HPR is NOT a compounded rate of return
• NO consideration for the time an investment was held
• CFP will typically not give you a straightforward HPR because it is very straight forward
• Items that make the computation more difficult:
  ○ Dividends received (ADD Cash Flow)
  ○ Margin Interest paid (SUBTRACT Cash Flow)
  ○ Taxes PAID (SUBTRACT Cash Flow)
  § ONLY if the question asks for the after-tax gain
  or loss.
  § Taxes computed based on the dividends
  received and any capital gains on the sale (ST vs
  LT)
  ○ Purchased Securities on Margin
  § SUBTRACT any interest paid on amount
  borrowed (NUMERATOR)
  § SUBTRACT the total cost of the securities
  (Amount borrowed) from Selling Price
  (NUMERATOR)
  § INCLUDE equity in the trade in the
  DENOMINATOR

Question 2

Effective Annual Rate (EAR = EFF%)

Answer 2

• This formula calculates the Effective Annual Interest Rate Earned on an investment when compounding occurs more often than ONCE PER YEAR.
• Calculator Keystrokes:
  ○ Nominal Rate [ORANGE] [NOM%]
  ○ # of compounding [ORANGE] [P/YR]
  ○ [ORANGE] [EFF%] = EAR

Question 3

Arithmetic Average

Answer 3

• Arithmetic Average = MEAN or “simple average”
• It is the sum of all numbers divided by the number of observations
• Calculator Keystroke = [ORANGE][ x , y (with line on top of letter)]

Question 4

Geometric Average (formula provided)

Answer 4

• This is the standard formula for finding the geometric mean for a set of observations, where a1, a2, a3, etc. may represent a set of given stock prices over a period of time.
• Time-Weighted Compounded Rate of Return

Question 5

Weighted Average

Answer 5

• Can be used to calculate a weighted average
  ○ share price,
  ○ expected returns,
  ○ Beta
  ○ Duration.
• The process is the same regardless of what is being calculated.

Question 6

Net Present Value

Answer 6

• NPV is used to evaluate capital expenditures that will result in differing cash flows over the useful life of investment period
• NPV = Deterministic
  ○ NPV = Positive ==> Good Investment
  ○ NPV = Negative ==> Bad Investment
• NPV = PV of CF - Initial Cost

Question 7

Internal Rate of Return (IRR)

Answer 7

• IRR is the discount rate that sets the NPV formula equal to ZERO
• IRR = compounded rate of return
• IRR should be calculated when you have uneven CF and you are asked to calculate the compounded rate of return.

Question 8

Dollar Weighted Return (IRR)

Answer 8

• Calculate IRR using the INVESTOR’s CF
• This calculation would take into account additional share purchases, as it is looking for investor returns

Question 9

Time Weighted Return (IRR)

Answer 9

• KNOW that MF reports are on a time weighted basis
• Calculate IRR using the SECURITY’s CF. Assume a buy and hold
• This calculation would not take into account additional share purchases. It is concerned with the growth of a since share or single purchase, since it is concerned with the securities CF, not the investor.
• Determined WITHOUT regard to the investors CF

Question 10

Arbitrage Pricing Theory (APT)

Answer 10

• APT assets that pricing imbalances CANNOT exist for any significant period of time; otherwise investors will exploit the price imbalance until the market prices are back to EQUILIBRIUM
• APT is a multi-factor model that attempts to explain return based on factors.
  ○ Anytime a factor has a value of ZERO, then the
  factor has NOT IMPACT ON RETURN
• APT attempts to take advantage of pricing imbalances
• Inputs are factors (F) such as:
  ○ Inflation
  ○ Risk premium
  ○ Expected returns and their sensitivity (b) to the
  factors.
• NOT INPUTS:
  ○ Beta
  ○ Standard Deviation
• Ri = a1 + b1F1 + b2F2 + b3F3 + e

Question 11

Foreign Currency Translation

Answer 11

• Investors may purchase as asset that is denominated in a foreign currency, so their return is affected by the growth of the security they purchase and the relative growth of the foreign currency and the US dollar
• To solve these problems, follow these steps:
  ○ Covert US dollar to the foreign currency to
  determine the cost
  ○ Compute the return, typically utilizing the HPR
  calculation
  ○ Covet the foreign currency back to the US dollar.

EXAMPLE on pg. 61