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CFA Notes > Interest Rates > Flashcards

Interest Rates Flashcards

Pre-requisite & Core

1
Q

What is an Interest Rate (r)?

A

A rate of return which reflects the difference between differently dated cashflows

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2
Q

If £9,500 today and £10,000 in 1.0 years are equivalent in value, what is the interest rate?

A

r = (10,000-9,500) / 9,500

= 0.0526 / 5.26%

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3
Q

What are three interchangeable names for interest rates?

A

1.) Required rate of return
2.) Discount rate
3.) Opportunity cost

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4
Q

What are the 4 premiums above risk free rate of interest?

A

1.) Inflation premium
2.) Default risk premium
3.) Liquidity premium
4.) Maturity premium

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5
Q

What is the inflation premium?

A

Compensation for expected inflation over the duration of the debt. Risk free rate + Inflation premium = Nominal risk free rate

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6
Q

What is the liquidity premium?

A

Compensation for the risk of loss relative to fair value, if an investment has to be quickly converted to cash

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7
Q

What is the default risk premium?

A

Compensate investors for the possibility that the borrower will - default/make incorrect/miss - payments.

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8
Q

What is the maturity premium?

A

Compensate investors for increased sensitivity of the market value of debt over time - longer debt = > risk and premium.

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9
Q

What is the equation for the future value of £100 invested for 1yr @ 5%

A

FV1 = PV(1+r) //// FV1 = £100(1+0.05)

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10
Q

What is the equation for the future value of £100 for 100yrs @ 5%

A

FVn = PV(1+r)^n //// FV100 = £100(1+0.13) ^100 = £20,316,287.

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11
Q

What is the future value of £5m for 5 yrs @ 7%

A

FVn = PV(1+r)^n ////// FV5 = £5m(1+0.07)^5 = £7,012,758

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12
Q

If the stated interest (rs) is 8% compounded periodically, how does that impact the FV formula?

A

FVn = PV (1 + rs / no. annual compounds) ^ no.annual compounds * n

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13
Q

What is the formula for FV on a continuously compounded rate?

eg., £5,000 - 8% - 2yrs

A

FVn = PVe^rsn

FV2= PV * e ^ 0.08 * 2

= £5,867.55

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14
Q

How do you calculate the Effective Annual Rate where the stated interest is 8% but the security compounds monthly?

A

EAR = ( 1 + periodic rate) ^m -1

= (1 + 0.08/12)^12 -1

= 0.08299951

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15
Q

Calculate the stated interest rate where the EAR (effective annual rate) is 8.299951% compounded monthly

A

EAR = ( 1 + periodic rate ) ^m -1
0.08299951 = (1+pr)^12 -1
1.08299951 = (1+pr)^12
1.08299951^1/12=1+pr
1 - (1.08299951) ^1/12 = pr
periodic rate = 0.0066667
rs = pr *12
= 8%

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16
Q

If you are asked to calculate the FV of a sum which has many or continuous compounding periods within a year, what is the process?

A

Calculate the EAR -
(continuous) EAR = e^rs(n) -1
(periodic) EAR = (1 + periodic rate e.g., 0.08/12) ^12 -1

Then do FV

FVn = PV(1+r)^n

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17
Q

What is an annuity?

A

A set of level/identical and sequential cashflows

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18
Q

What is an ordinary annuity?

A

An annuity which has its first cashflow 1 period from now - indexed at t = 1

19
Q

What is an annuity due?

A

An annuity due has its first cashflow immediately - indexed at t = 0

20
Q

What is a perpetuity / annual perpetuity?

A

A set of level/identical, never-ending cashflows where the first cashflow is 1 period from now - indexed at t = 1

21
Q

What is the equation to simply calculate the future value of an ordinary annuity over e.g., 20 years, 20k pa, @ 9%

A

FVn = A ((1+r)^n -1) / r)
FVn = 20,000 (1+0.09)^20 -1 / 0.09)

22
Q

What is the formula for PV?

A

PV = FVn (1/(1+r)^n)

23
Q

What is the formula for PV with periodic compounding?

A

PV = FVn (1 + rs/m)^-m * n

24
Q

The manager of a Canadian pension fund knows that the fund must make a lump-sum payment of C$5 million 10 years from now. She wants to invest an amount today in a GIC so that it will grow to the required amount. The current interest rate on GICs is 6 percent a year, compounded monthly. How much should she invest today in the GIC?

A

PV = FVn (1 + rs/m)^-m*n

PV = 5,000,000 ( 1 + 0.06/12)^-12*10

PV = 2,748,163.67

25
Q

What the equation for the present value of an annuity?

A

PV = A ( 1 - 1/(1+r)^n / r)

26
Q

Suppose you are considering purchasing a financial asset that promises to pay €1,000 per year for five years, with the first payment one year from now. The required rate of return is 12 percent per year. How much should you pay for this asset?

A

PV = A (1- 1/(1+r)^n / r)
PV = 1000 (1 - 1/(1+0.12)^5 / r)
PV = £3,604.78

27
Q

You are retiring today and must choose to take your retirement benefits either as a lump sum or as an annuity. Your company’s benefits officer presents you with two alternatives: an immediate lump sum of $2 million or an annuity with 20 payments of $200,000 a year with the first payment starting today. The interest rate at your bank is 7 percent per year compounded annually. Which option has the greater present value? (Ignore any tax differences between the two options.)

A

$2m today = $2m today

It’s an annuity due, 1st payment is today.

Therefore £200k lump sum + PV of 19 yrs $200k ordinary annuity

PV = A (1 - 1/(1+r)^n / r)
PV = 200,000 (1 - 1/(1+0.07)^19 / 0.07)
PV = £2,267,119.05

Therefore annuity payments are superior

28
Q

A German pension fund manager anticipates that benefits of €1 million per year must be paid to retirees. Retirements will not occur until 10 years from now at time t = 10. Once benefits begin to be paid, they will extend until t = 39 for a total of 30 payments. What is the present value of the pension liability if the appropriate annual discount rate for plan liabilities is 5 percent compounded annually?

A

Draw a timeline.
t 0——9————-39
$ 0——1————30

Calculate the annuity of the 30 payments of 1m from yr 10 to 39

PV=1,000,000 (1- 1/(1.05)^30/0.05)
PV @ yr 9 = $15,372,451
Then PV to yr0
PV = FVn(1+r)^-n
PV = $15,372,451 (1.05)^-9
= £9,909,219

29
Q

What is the equation for a perpetual annuity?

A

PV = (A / r)

30
Q

Consider a level perpetuity of GBP100 per year with its first payment beginning at t = 5. What is its present value today (at t = 0), given a 5 percent discount rate?

A

Calculate the £100 in perp from yr 5 =
1/r * 100
step 2:
Calculate PV as if it is its own Ordinary annuity therefore PV from yr 4 -

PV = 2000 ( 1/(1+r)^4 = £1,645.40 @ t = 0.

31
Q

What is the equation for a growth rate?

A

g = (FVn / PV) ^1/n

32
Q

Toyota Motor Corporation, one of the largest automakers in the world, had consolidated vehicle sales of 8.96 million units in 2018 (fiscal year ending 31 March 2018). This is substantially more than consolidated vehicle sales of 7.35 million units six years earlier in 2012. What was the growth rate in number of vehicles sold by Toyota from 2012 to 2018?

A

g = (FVn/PV)^1/n
g= (8.96/7.35)^1/6
g= 3.36%

33
Q

Can a lump sum be an annuity?

A

Yes and an annuity can be seen as equivalent to future value. PV’s FV’s and series of cashflows can all be equivalent if they are indexed at the same point in time.

34
Q

What is the Cash Flow Addivity Principle?

A

The cash flow additivity principle—the idea that amounts of money indexed at the same point in time are additive—is one of the most important concepts in time value of money mathematics.

35
Q

What is the equation for a holding period return?

A

The following reflects return over time inclusive of capital appreciation and income.

HPR = (p1 - p0) + total income / p0

36
Q

An investor purchased 100 shares of a stock for USD34.50 per share at the beginning of the quarter. If the investor sold all of the shares for USD30.50 per share after receiving a USD51.55 dividend payment at the end of the quarter, the investor’s holding period return is closest to:

−13.0 percent.
−11.6 percent.
−10.1 percent.

A

-10.1%

37
Q

What mean should you use when including all values and outliers?

A

Arithmetic Mean

38
Q

What mean should you use when calculating compounding?

A

Geometric Mean

39
Q

What mean should you use when calculating mean where data has multiple extreme outliers?

A

Harmonised Mean, Winsorized Mean and Trimmed Mean

40
Q

What is the definition of IRR?

A

The internal rate of return is the discount rate at which the sum of present values of cash flows will equal zero.

41
Q

what do you calculate when you want the money weighted return of a fund?

A

IRR

42
Q

When use IRR (money weighted return) or geomean (time weighted return)?

A

IRR is best for calculating the return of an investment including its inflows and outflows, e.g, Real Estate

Time weighted return does not account for in/outflows and therefore better reflects the performance of a fund from a portfolio manager perspective.

43
Q

What is a gross return?

A

The return earned by an asset manager prior to deductions for management costs, custodial fees, or expenses related to administration of an investment. Trading expenses (commission) are included in gross return, they do relate to an asset managers performance.

44
Q
A

CFA Notes (4 decks)

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