Summary Complete CFA L3 formula sheet

CFA LEVEL III 2025 FORMULA SHEET




F in Q uiz F ormula S heet CFA P rogram L evel III
VOLUME 1: ASSET ALLOCATION


π# , π"32:#" = respectively the expected and 1. Expected Rate of Return On Equity
Learning Module 1: target inflation rates E(R e ):
Capital Market Expectations, Part 1: 7 7 "2#08 = respectively the expected and
Y# , Y <
E (Re) ≈ = + (% ∆E − %∆S) + ∆P/E
Framework and Macro Considerations trend real GDP growth rates
Where,
By readjusting the above equation:
1. Aggregate Market Value of Equity: o E (Re) = Expected rate of return on
V"# = GDP" × S"+ × PE" 3. Real inflation adjusted target rate equity
o D/P = Expected dividend yield
Where, o %∆S = Expected % change in number
o GDP is a level of nominal GDP 7# − Y
i∗ − π# = r0#1"234 + 0.5 × (Y 7 "2#08 )+ of shares outstanding
o S"+ is the share of profits in the 0.5 × (π# – π"32:#" )
economy 2. Under Basic CAPM model
4. Net exports:
o PE" is the P/E ratio.
= Net Private Savings + Government a) 𝑅𝑃@ = 𝛽@,C 𝑅𝑃C
Surplus M
2. Taylor Rule: b) 𝛽@,C = 𝐶𝑜𝑣(𝑅@ , 𝑅C )/𝜎CJ = 𝜌@,C @ LM N P
O
(X–M) = (S–I) + (T-G)
7# - Y
i∗ = r0#1"234 + π# + 0.5 × (Y 7 "2#08 )+ 0.5 Where,
× (π# – π"32:#" ) 5. Government Surplus: 𝑅𝑃@ = [𝐸𝑅@ − 𝑅S ] risk premium on ith
asset
Where, = Taxes – Government spending 𝑅𝑃C = [𝐸𝑅C − 𝑅S ] risk premium on
market portfolio
i∗ = target nominal policy rate Learning Module 2 𝛽@,C = ith asset sensitivity to market
UVW(XN ,XO) M
rneutral = real policy rate that would be Capital Market Expectations, Part 2: portfolio = Y = 𝜌@,C LM N P
MO
targeted if GDP growth were on trend & Forecasting Asset Class Returns O

inflation on target 𝜎 is standard deviation and ρ is correlation



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, CFA LEVEL I 2025 FORMULA SHEET


Learning Module 3
3. Expected Return using Singer-Terhaar ƒEquity 8 − Equity † ‡ + ƒLiquid8 − Overview of Asset Allocation
Model: Liquid† ‡

10. 𝑟@ = 𝛼@ + ∑•’–— 𝛽@’ 𝐹’ + 𝜀@
Model’s 1st component (full integration 1. Risky Asset Allocation
assumption): 1 𝜇 − 𝑟·
𝑟@ = return on ith asset = 𝑤∗ = µ J ¸
𝛼@ = constant intercept 𝜆 𝜎
X=fO
4. 𝑅𝑃@e = 𝛽@,eC 𝑅𝑃eC = 𝜌@,eC 𝜎@ L P 𝛽@’ = asset’s sensitivity to kth factor
MfO
𝐹’ = kth common factor return Learning Module 4
Model’s 2nd
component (completely 𝜀@ = error term Principles of Asset Allocation
segmented market assumption):
opr
11. 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑛 𝑖𝑡ℎ 𝑎𝑠𝑠𝑒𝑡
5. RPhi = 1 × RPkl = 1 × σh n q
t = 𝜎@ J = ∑•¡–— ∑•¢–— 𝛽@¡ 𝛽£¢ 𝜌¡¢ + 𝑣@J
sq 1. Investor’s Utility for Asset Mix
J
𝑈¡ = 𝐸(𝑅¡ ) − 0.005𝜆𝜎¡
6. 𝑅𝑃@ = 𝜑𝑅𝑃@e + (1 − 𝜑)𝑅𝑃@w where,
𝜌¡¢ = covariance between the mth and 2. Risk Parity
x122#0" y#32z { |}~ nth factor 1 J
7. Cap rate =
p2•€#2"y •341# 𝑣@J = variance of ith asset return 𝑤@ × 𝐶𝑜𝑣 (𝑟@ , 𝑟= ) = 𝜎
𝑛 =
3. Marginal contribution to risk (𝑀𝐶𝑇𝑅@ )
where NOI = net operating Income 12. Covariance between ith and jth = (Beta of Asset Class i relative to
= 𝜎@£ = ∑•¡–— ∑•¢–— 𝛽@¡ 𝛽£¢ 𝜌¡¢ Portfolio) x (Portfolio Std. Dev.)
8. E(Rre) = Expected return on real estate
• long run (assuming constant growth 13. 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑟𝑒𝑡𝑢𝑟𝑛 4. Absolute contribution to risk (𝐴𝐶𝑇𝑅@ )
rate for NOI) is: = 𝑅¥ = (1 − 𝜆)𝑟¥ + 𝜆 𝑅¥§— = 𝐴𝑠𝑠𝑒𝑡 𝑐𝑙𝑎𝑠𝑠 𝑤𝑒𝑖𝑔ℎ𝑡@ x 𝑀𝐶𝑇𝑅@
where 𝜆 𝑚𝑎𝑦 𝑟𝑎𝑛𝑔𝑒 𝑓𝑟𝑜𝑚 0 𝑡𝑜 1
E(Rre) = Cap rate + NOI growth rate 5. Portfolio Std. Dev. (expected)
—-®
14. 𝑣𝑎𝑟 (𝑟) = L—§®P 𝑣𝑎𝑟(𝑅) > 𝑣𝑎𝑟(𝑅) = Sum of ACTR = ∑¢@ 𝐴𝐶𝑇𝑅
• for a finite horizon (to reflect
expected rate of change in the cap
15. ARCH Methodology 6. % contribution to total Standard
rate) is:
Deviation
𝜎¥J = 𝛾 + 𝛼𝜎¥§—
J
+ 𝛽𝜂¥J ÀUÁXN
= =VÂ¥·VÃ@V w¥Ä.<ÅW
E(Rre) = Cap rate + NOI growth rate -
%Δ Cap rate
Rearranging the above equation:
𝜎¥J = 𝛾 + (𝛼 + 𝛽)𝜎¥§—
J
+ 𝛽(𝜂¥J − 𝜎¥§—
J
) 7. Ratio of excess return to MCTR
9. Implication of capital mobility: ƒÆÇÈÅÉ¥ÅÄ Xťʢ§XË ‡
Eƒ%∆S8/† ‡ = ƒr 8 − r † ‡ + ƒTerm8 − =
CUÁX
Term† ‡ + ƒCredit 8 − Credit † ‡ +



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