Learning Module 2 of Quantitative Methods 11–14% of the exam

Types of Financial Returns

3 lessons. About 15 minutes in cram mode, 78 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary Practice this module

Lessons

1
Types of returns: assets, instruments and indicators
calculate 6 min cram, 30 min full
2
Long-run asset class returns and their components
compare 4 min cram, 22 min full
3
Macro and micro risk and the risk-return trade-off
compare 5 min cram, 26 min full

What the exam expects you to do

Calculate, compare, and interpret different types of returns for financial assets, instruments, and indicators.Types of returns: assets, instruments and indicators

Module summary

The whole module on one sheet, organised by lesson: what to memorize, how the ideas fit together, the formulas and the key terms. No paragraphs, just what you need to revise.

Hide what I know

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

Types of returns: assets, instruments and indicators

Known

MemorizeReturn types and the two formulas

Item	Rule
Price return	Change in price; uncertain
Fixed capital distribution	Set in advance; most debt
Variable capital distribution	Dividends, floating-rate coupons
Bill, annualized	$(\text{Face}/\text{Price})^{365/\text{days}} - 1$
Foreign asset, home currency	$(1 + r_{local})(1 + r_{currency}) - 1$

Memory hook Bills: divide, power, minus one. Currency: multiply the growth factors, never add.

Know it cold Indicators (rates, exchange rates, indexes) pay no cash. You earn them through assets, instruments or funds.

Key terms

price return Memorize
capital distribution return Memorize
total return Memorize
fixed capital distribution return Memorize
variable capital distribution return Memorize
financial asset Use it
cash Know the idea
equity Use it
bond Use it
amortizing bond Know the idea
hybrid Know the idea
financial instrument Use it
derivative Know the idea
financial indicator Use it
interest rate Use it
risk-free rate Use it
discount instrument Use it
foreign exchange rate Use it
currency pair Know the idea
market index Use it
home-currency return Memorize

Where a return comes from

Total returnprice return plus capital distribution return

Price return Memorize the change in price, independent of any payout; uncertain
Capital distribution return Memorize the cash paid to the holder
- Fixed set in advance; most bond coupons
- Variable changes over time; dividends, floating-rate coupons

Financial assets and what they pay

Financial assets

Cash pays nothing until it is invested
Equity price return plus variable dividends
Bonds fixed coupons plus principal; price moves with rates and credit
- Amortizing bond principal repaid in installments
Hybrids preferred stock, convertible bonds

Assets, instruments and indicators

Where returns are found

Financial assets Use it cash, equity, bonds, hybrids
Financial instruments Use it standardized agreements that let assets trade
- Cash instruments shares and bonds
- Derivatives value comes from an underlying asset or indicator
- Securitized debt
Financial indicators Use it pay no cash of their own
- Interest rates and the risk-free rate
- Foreign exchange rates
- Market indexes

Formulas

Total return: price plus distribution Memorize

r = \frac{P_1 - P_0 + \text{Inc}}{P_0} = \frac{P_1 - P_0}{P_0} + \frac{\text{Inc}}{P_0}

Quick example

Buy at 60.00, receive a 1.50 dividend, sell at 63.00. (63.00 − 60.00 + 1.50) ÷ 60.00 = 7.5%: price return 5.0% plus distribution return 2.5%.

On your calculator

63−60+1.5=÷60= 0.075

63ENTER60−1.5+60÷ 0.075

ENTER enter (on the HP, puts the number on the stack)

Government bill: return over its life Memorize

r_{period} = \frac{\text{Face}}{\text{Price}} - 1

Quick example

A 182-day bill with face value 10,000 is priced at 9,780. 10,000 ÷ 9,780 − 1 = 2.2495% over its life.

On your calculator

10000÷9780−1= 0.0225

10000ENTER9780÷1− 0.0225

ENTER enter (on the HP, puts the number on the stack)

Government bill: annualized return Memorize

r_{annual} = (1 + r_{period})^{365/\text{days}} - 1

Quick example

The same 182-day bill. 1.022495 raised to 365 ÷ 182, minus 1, is 4.56%. Doubling the period return would give 4.50%.

On your calculator

10000÷9780=y^x(365÷182)=−1= 0.0456

y^x power

10000ENTER9780÷365ENTER182÷y^x1− 0.0456

ENTER enter (on the HP, puts the number on the stack) · y^x power

Currency return Use it

r_{currency} = \frac{S_1}{S_0} - 1

Quick example

The home-currency price of one unit of the foreign currency rises from 0.9200 to 0.9568. 0.9568 ÷ 0.9200 − 1 = +4.00%.

On your calculator

0.9568÷0.92−1= 0.04

0.9568ENTER0.92÷1− 0.04

ENTER enter (on the HP, puts the number on the stack)

Foreign asset in your home currency Memorize

r_{home} = (1 + r_{local})(1 + r_{currency}) - 1

Quick example

Local return 5.0%, and the foreign currency falls 3.0% against yours. 1.05 × 0.97 − 1 = 1.85%.

On your calculator

1.05×0.97−1= 0.0185

1.05ENTER0.97×1− 0.0185

ENTER enter (on the HP, puts the number on the stack)

Geometric mean return Memorize

r_G = \left[(1 + r_1)(1 + r_2)\cdots(1 + r_n)\right]^{1/n} - 1

Quick example

Returns of +30% and −20%. The arithmetic mean is 5.00%. (1.30 × 0.80)^(1/2) − 1 = 1.98%.

On your calculator

1.3×0.8=y^x0.5=−1= 0.0198

y^x power

1.3ENTER0.8×0.5y^x1− 0.0198

ENTER enter (on the HP, puts the number on the stack) · y^x power

Long-run asset class returns and their components

Known

MemorizeThe long-run record (no figures needed)

Asset class	Long-run return	Mostly from
Equities	Highest	Price appreciation
Bonds	Middle	Coupons (capital distributions)
Short-term bills	Lowest, about inflation	Interest (the discount)

Memory hook Shares grow, bonds pay, bills keep pace.

Know it cold Compare two returns with $(1 + r_A)/(1 + r_B) - 1$ , not by subtracting when options are close.

Key terms

long-run asset class returns Memorize
large-cap equities Know the idea
small-cap equities Know the idea
corporate bonds Know the idea
government bonds Know the idea
short-term government bills Know the idea
capital appreciation return Use it
relative outperformance Memorize
small-cap premium Know the idea
default effect Know the idea
maturity effect Know the idea
real return Use it
share buybacks Know the idea
limits of historical returns Use it

Long-run returns, highest to lowest

Long-run asset class returnsa pattern across long periods, not a promise for any one year

Equities Memorize highest; mostly price return
- Large caps ahead of small caps in the curriculum's US sample
- Small caps a premium in some periods, fading over time
Bonds Memorize middle; mostly coupons
- Government bonds longer maturity earned more than shorter
- Corporate bonds higher promised yield, but defaults cut realized return
Short-term government bills Memorize lowest; about inflation, so real return near zero

Where long-run returns come from

Long-run total return

Price return Memorize dominant for equities; volatile; lifted by buybacks
Capital distribution return Memorize dominant for bonds; tracks the level of interest rates; dividends trending down

Formulas

Relative outperformance (ratio form) Memorize

r_{rel} = \frac{1 + r_A}{1 + r_B} - 1

Quick example

Equities earn 10.4% a year and bonds 7.1%. 1.104 ÷ 1.071 − 1 = 3.08% a year. The simple difference, 3.30%, overstates it.

On your calculator

1.104÷1.071−1= 0.0308

1.104ENTER1.071÷1− 0.0308

ENTER enter (on the HP, puts the number on the stack)

Macro and micro risk and the risk-return trade-off

Known

MemorizeRisk families and the trade-off

Risk	Also called	Diversifiable?	Examples
Macro	Systematic	No	Inflation, interest rate, market
Micro	Unsystematic	Yes	Issuer (business, financial, credit), sector

Memory hook Macro hits the whole market, micro hits one name. I-R-M: inflation, rates, market.

Know it cold Wider range = more risk. $r_{portfolio} = \sum w_i r_i$ , for total, price and distribution returns alike.

Key terms

macro risk Memorize
systematic risk Memorize
inflation risk Memorize
interest rate risk Memorize
market risk Memorize
micro risk Memorize
unsystematic risk Memorize
issuer risk Memorize
business risk Memorize
financial risk Memorize
credit risk Memorize
sector risk Memorize
range of annual returns Use it
risk-return trade-off Use it
market risk premium Use it
portfolio return Memorize

Sources of investment risk

Riskthe gap between the return you expect and the one you get

Macro risk Memorize systematic; cannot be diversified away
- Inflation risk returns miss expectations because of inflation or deflation
- Interest rate risk prices fall when rates rise, and rise when rates fall
- Market risk market-wide forces move all assets unexpectedly
Micro risk Memorize unsystematic; can be diversified away
- Issuer (specific) risk Memorize depends on one firm
  - Business riskfrom the nature of operations
  - Financial riskfrom using debt; includes credit risk
- Sector (industry) risk Memorize forces particular to one sector

Why return rises with risk

Prices adjust until return fits risk

Too much return for the risk buyers rush in
- Price is bid up
  - Expected return falls
Too little return for the risk investors sell
- Price falls
  - Expected return rises

Formulas

Range of annual returns Use it

\text{Range} = r_{best} - r_{worst}

Quick example

An asset's best year is +18% and its worst is −9%. The range is 18 − (−9) = 27 percentage points.

On your calculator

18−9+|-= 27

+|- change sign

18ENTER9CHS− 27

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Market risk premium (ratio form, exact) Use it

\text{MRP} = \frac{1 + E[r_m]}{1 + r_f} - 1

Quick example

Expected market return 6.5%, risk-free rate 2.0%. 1.065 ÷ 1.02 − 1 = 4.41%.

On your calculator

1.065÷1.02−1= 0.0441

1.065ENTER1.02÷1− 0.0441

ENTER enter (on the HP, puts the number on the stack)

Market risk premium (difference form, approximate) Use it

\text{MRP} \approx E[r_m] - r_f

Quick example

The same inputs: 6.5% − 2.0% = 4.50%. It is 0.09 percentage points above the exact 4.41%.

On your calculator

6.5−2= 4.5

6.5ENTER2− 4.5

ENTER enter (on the HP, puts the number on the stack)

Portfolio return Memorize

r_{portfolio} = w_1 r_1 + w_2 r_2 + \cdots + w_N r_N = \sum_{i=1}^{N} w_i r_i

Quick example

50% in equities at 8.8%, 35% in bonds at 5.4%, 15% in bills at 2.2%. 4.40 + 1.89 + 0.33 = 6.62%.

On your calculator

(0.5×8.8)+(0.35×5.4)+(0.15×2.2)= 6.62

0.5ENTER8.8×0.35ENTER5.4×+0.15ENTER2.2×+ 6.62

ENTER enter (on the HP, puts the number on the stack)