Lesson 3 of Investment Planning: Measuring Return

Question 1

Holding Period Return Formula

Not given on the exam

Answer 1

Question 2

Holding Period Return!

Answer 2

• Holding Period return is not a compounded rate of return.
• There is no consideration for the time an investment was held.

Exam Tip:

• It is possible HPR questions may come from margin returns or after-tax rate of returns.

Question 3

Holding Period Return Calculation Notes

Answer 3

The examiners will typically not give you a straight computation because it is straight forward, and will include more difficult options.

• Dividends received: Make sure to add them to the numerator.
• Margin Interests Paid: Make sure to subtract from the numerator.
• Taxes paid: Only do this if the question asks for the after-tax gain or loss. The taxes will be computed based on the dividends received and any capital gains on the sale (short-term versus long-term). Taxes, like margin interest, are subtracted from the numerator.
• Purchased the Securites on Margin:
  • In the numerator make sure to subtract any interest paid.
  • Also, in the numerator you will include the total cost of the securities as a subtraction from the sales proceeds.
  • In the denominator you only include your equity in the trade.

Question 4

Example 1 of HPR

• No Tax

Answer 4

Question 5

Example 2 HPR

• With Tax

Answer 5

Question 6

The 2nd Holding Period Return Formula

FORMULA PROVIDED

Answer 6

• Another method of calculating HPR when provided with period returns instead of cash flows.

r = % return per period

n = number of periods.

Question 7

Example of HPR Equation Problem

Answer 7

Question 8

Effective Annual Rate!

Answer 8

• This formula calculates the effective annual interest rate
  
  • earned on an investment
  • when the compounding occurs more often than once per year.

Question 9

Effective Annual Rate (EAR) Formula

Formula Given on Exam

Answer 9

i = states annual interet rates
n = number of compounding periods

Question 10

EAR Example

Answer 10

EXAM TIP: Earning 10% compounded quarterly is equivalent to earning 10.38% compounded annually.

Question 11

Nominal Rate of Interest

Answer 11

• Nominal interest rate refers
  
  • to the interest rate before taking inflation into account.
  • Nominal can also refer to the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest.

Question 12

Arithmetic Average!

Answer 12

The artithmetic average (or mean) is also known as the simple average.

• It is the sum of all numbers divided by the number of observations.
• The artithmetic average (or mean) is a simple calculation.
• However, when determining the average rate of return of an investment over time, it may give a misleading result.
• That is because the artithmetic average (or mean) ignores the compounding effect over time.

Question 13

Artithmetic Average Formula

Formula Given on Exam

Answer 13

Question 14

AM Example

Answer 14

What is the average price of the three stocks below?

Stock X Price: $12
Stock Y Price:$15
Stock Z Price: $27

( 13 + 15 + 27 ) ÷ 3
=$18

Calculate in Calculator like you are solving for Standard Deviation except calculate x with the bar.

Question 15

Geometric Average!

Answer 15

• The geometic average, or geometric mean,
  
  • is also a time weighted compounded rate of return.
• Simply stated, the geometric average is the compounded rate of return.

Question 16

Geometric Average Formula for Set of Observations

Not Given on Exam

Answer 16

• This is the standard formula for finding the geometric average mean for a set of observations, where a1, a2, a3, etc may represent a set of given stock prices over a period of time.
• It is important to note that the standard formula may not be appropriate when calculating the geometric mean return given a time series of asset returns. That is because of the possibility of earning a negative or a 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 negative number. A zero return also creates issues.

Question 17

Example of GM for Observations

Answer 17

Question 18

Geometric Mean for Returns Formula

Provided on the Exam

Answer 18

• The multiplying 100 should be after you get an answer to convert to a percentage.
• the minus one should be outside the square root.

Question 19

Example of Geometric Mean for Returns

Answer 19

Question 20

Weighted Average!

Answer 20

A weighted average

• can be used to calculate the average share price, expected returns, beta, or duration.
• The process is the same regardless of what is being calculated.

For Weighted Avergage Portfolio return and weighted average portfolio beta

• tell you the risk and return on a proportionate basis per unit of investment.

Question 21

Weighted Average Share Price

Answer 21

• The weighted average takes into account
  
  • the number of shares of each of the various priced securities that are owned.

Question 22

Weighted Average Share Price Formula

Not on exam

Answer 22

Σ( # of Shares x Price per share )
÷
( total number of shares )

Question 23

Weighted Average Share Price Example

Stock X on 1/12010 = 15 shares at $12 per share
Stock X on 2/1/2010 = 5 shares at $15 per share
Stock X on 3/1/2010 = 1 share at $27 per share

Answer 23

(15 x 12) + (5 x 15) + (1x27)
÷
(15+5+1)
=$13.42

Question 24

Weighted Average Portfolio Return

Answer 24

In the case of a portfolio calculation for the weighted average return, there are several facts that must be taken into account in the process of the calculation.

1. The current fair market value of the securities held.
2. The total portfolio value (TPV).
3. The return of each security throughout the period in question.

Question 25

Weighted Average Portfolio Return Example

Three securities, X, Y, and Z make up the portfolio. The shares of X in the portfolio have a market value of $10,000 and during the period returned 15%. Y has a market value of $15,000 and returned 12%. Z has a market of $25,000 and returned 10% over the period.

Answer 25

Question 26

Weighted Average Portfolio Beta!

Answer 26

• The calculation of a weighed average portfolio beta is not that different than that of the weighted average portfolio return.

Question 27

Weighted Average Portfolio Beta Example

Three securities, X, Y, and Z make up the portfolio. The shares of X in the portfolio have a market value of $10,000 and a beta of 1.3. Y has a market value of $15,000 and a beta of 0.80. Z has a market of $25,000 and a beta of 2.2.

Answer 27

Question 28

Net Present Value!

Answer 28

• Is used to evaluate capital expenditures that will result in different cash flows over the useful life or investment period.

NPV is deterministic.

• If the NPV is positive, the investor would make the investment.
• If the NPV is negative, the investor would not make the investment.
• If the NPV 0 investor should still make the investment.

NPV = PV of Cash Flows - Initial Cost

Question 29

NPV Example

A business is considering purchasing a piece of new equipment for $100,000. The equipment will generate the following revenues.

Year 1: $50,000
Year 2: $30,000
Year 3: $20,000
Year 4: $10,000

The machine can be sold at the end of year four for $25,000. Assume a discount rate of 8%. Should they purchase the new piece of equipment?

Answer 29

CF0 = <100,000>
CF1 = 50,000
CF2 = 30,000
CF3 = 20,000
CF4 = (10,000 + 25,000) = 35,000
I = 8%
NPV = $13,619

Business should purchase equipment because value of the cash flows exceed initial cost/investment.

Question 30

Compute NPV on Calculator

Answer 30

(1) Start by clicking the CF button for Cash Flows.

(2) Press 2nd Clear work to clear previous work.

(3) Input the CF0 into the calculator. Click enter when inputed. Reminder to use negative sign as this is your beginning purchase.

(4) Click the down arrow and enter C01.

(5) Click the down arrow and skip over F01 unless the frequency is more than once for that period.

(6) Repeat steps until information is put in.

(7) The click NPV.

(8) Enter discount rate amount. Put in as whole number percent. The click enter and press down arrow.

(9) To calculate NPV click CPT button.

Question 31

Internal Rate of Return!

Answer 31

• IRR is the discount rate that sets the NPV formula equal to zero.
• NPV = PV of Cash Flows - Initial Cost
• IRR can also be thought of as a compounded rate of return.
• IRR should be calculated when you have uneven cash flows and you are asked to calculate a compounded rate of return.

Question 32

IRR Example

A business is considering purchasing a piece of new equipment for $100,000. The equipment will generate the following revenues.

Year 1: $50,000
Year 2: $30,000
Year 3: $20,000
Year 4: $10,000

The machine can be sold at the end of year four for $25,000. Assume a discount rate of 8%. Should they purchase the new piece of equipment?

Answer 32

CF0 = <100,000>
CF1 = 50,000
CF2 = 30,000
CF3 = 20,000
CF4 = (10,000 + 25,000) = 35,000
IRR = 14.63%

Intuitively, we should have expected a return greater than 8% because NPV was positive. Recall that a discount rate of 8% yielded a positive NPV.

Question 33

NPV AND IRR RULES

IF NPV is Positive, then
IF NPV is Zero, then
IF NPV is negative, then

Answer 33

• then IRR > Discount rate
• then IRR = Discount rate
• then IRR < Discount Rate

Question 34

Another IRR Example

Answer 34

Sydney buys a stock at $40 and it pays the following dividends.

Year 1: $2.00
Year 2: $2.50
Year 3: 0
Year 4: $2.75
What is Sydney’s compounded rate of return if the stock can be sold for $45 in year 4.

CF0 <40.00>
CF1 2.00
CF2 2.50
CF3 0
CF4 2.75 +45

Question 35

Compute IRR on Calculator

Answer 35

(1) Start by clicking the CF button for Cash Flows.

(2) Press 2nd Clear work to clear previous work.

(3) Input the CF0 into the calculator. Click enter when inputed. Reminder to use negative sign as this is your beginning purchase.

(4) Click the down arrow and enter C01.

(5) Click the down arrow and skip over F01 unless the frequency is more than once for that period.

(6) Repeat steps until information is put in.

(7) The click IRR

(8) The click CPT and IRR should be displayed.

Question 36

Dollar-Weighted Return!

Answer 36

• Calculates IRR using the investor’s cash flows.
• This calculation would take into account additional share purchases, as it is looking for investor returns.

Exam Tip: This is all about the investor.

Question 37

Dollar-Weighted Return Example

Bob purchases 1 share of DIS for $50. One year later the stock pays a dividend of $4 and Bob purchases an additional share for $65. Bob sold the stock one year later for $75 per share. What was Bob’s dollar-weighted return?

Answer 37

• Solve on calculator the same way.
• Use IRR, include cash flows with more than one negative.

Question 38

Time-Weighted Return!

Answer 38

• Calculates IRR using the security’s cash flow. Assumes 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 purchases, since it is concerned with the securities cash flow, not the investor.
• Determined without regard to the investor’s cash flows.
• Mutual fund report on a time-weighted return basis.

Exam TIp:

• Look at the beginning of the timeline and end to see when it was bought and sold for. And then look in the middle for dividends.

Question 39

Time-Weighted Return Example

Bob purchases 1 share of DIS for $50. One year later the stock pays a dividend of $4 and Bob purchases an additional share for $65. Bob sold the stock one year later for 75 per share. What was Bob’s dollar-weighted return?

Answer 39

Question 40

Exam Tip:

Answer 40

You may not have to calculate dollar-weighted or time-weighted return, but you must know that mutual funds report on a time-weighted basis.

Exam TIPS:

• Mutual Funds report on a time weighted basis.
• Understand the difference between time-weighted and dollar-weighted return and what variables are used for each.

Question 41

Arbitrage Pricing Theory (APT)!

Answer 41

• APT asserts that
  
  • pricing imbalances cannot exist for any significance 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 that factor has no impact on return.
• APT attempts to take advantage of pricing imbalances.
• Inputs are factors (F) such as
  
  • inflation,
  • risk premium, and
  • expected returns and
  • their sensitivity (b) to those factors.
• Standard deviation and beta are NOT inputs variables to the APT.

Question 42

APT Formula

Answer 42

Question 43

Exam Tip:

Answer 43

Don’t memorize the formula but make sure to know the bullet points and memorize the keywords:

• Multifactor model
• Sensitivity to the factors
• Standard Deviation + Beta are not inputs

Question 44

Foreign Currency Translation!

Answer 44

Investors may purchase an 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 foriegn currency and the U.S. dollar.

Question 45

Foreign Currency Translation Steps to Solve Problem

Answer 45

1. Convert the U.S. dollars to the foriegn currnecy to determine the cost.
2. Compute the return, typically utilizing the holding period return calculation.
3. Convert the foreign currency back to U.S. dollars.

Question 46

Foreign Currency Translation Example

Mr. Lampert wants to purchase 100 shares in Int. Easy, Co. He can purchase them in pounds sterling for £ 12.75 when the currency rate is $1.50/£ with the transaction costs of £25.00

(1) What will be his cost in sterling
(2) And in dollars?

If the stock increases to £17.50 per share, the transaction cost to sell is £25, and the currency rate is $1.55/£, what is Mr. Lampert’s gain in U.S. dollars?

Answer 46

(1) Cost in sterling = £12.75 x 100 + £25 = £1,300

(2) And in dollars = £1,300 x 1.50/£ = $1,950.

£17.50 x 100 - £25 = £1,725
£1,725 x $1.55/£ = $2,673.75

(2,673.75 - 1,950)
÷
1,950

= 37.11%