Free GARP FRM Part I Formula Sheet (2026)

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All FRM Part I Formulas

Foundations of Risk Management 12 items
Annual CDS premium payment
Premium=s×N\text{Premium} = s \times N
s = CDS spread (decimal), N = notional protected. Example: 250 bps on $800M = $20M/year
Expected loss on a credit exposure
EL=PD×LGD×EADEL = PD \times LGD \times EAD
PD = probability of default, LGD = loss given default, EAD = exposure at default
CAPM expected return
E[Ri]=Rf+βi(E[Rm]−Rf)E[R_i] = R_f + \beta_i (E[R_m] - R_f)
RfR_f = risk-free rate, βiβ_i = asset beta, E[RmR_m] = expected market return
CDS spread approximation
s≈PD×LGDs \approx PD \times LGD
s = annualized CDS spread, PD = annual probability of default, LGD = loss given default (1 − recovery)
Beta of an asset
βi=Cov(Ri,Rm)σm2\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2}
Cov(R_i,RmR_m) = covariance of asset and market returns, σmσ_m² = market return variance
Jensen's alpha
α=Rˉp−[Rf+βp(Rˉm−Rf)]\alpha = \bar R_p - [R_f + \beta_p(\bar R_m - R_f)]
R̄_p = realized portfolio return, RfR_f = risk-free rate, βpβ_p = portfolio beta, R̄_m = market return
Aggregate firm-wide economic capital variance
σfirm2=∑iσi2+2∑i<jρijσiσj\sigma_{firm}^2 = \sum_i \sigma_i^2 + 2\sum_{i<j} \rho_{ij}\sigma_i\sigma_j
σiσ_i = standalone EC of silo i, ρijρ_{ij} = pairwise correlation between silos i and j
Factor model return decomposition
Ri=E[Ri]+βi,1f1+⋯+βi,kfk+εiR_i = E[R_i] + \beta_{i,1}f_1 + \cdots + \beta_{i,k}f_k + \varepsilon_i
fkf_k = zero-mean factor surprise, βi,kβ_{i,k} = factor loading, εiε_i = idiosyncratic noise
Risk-adjusted return on capital (RAROC)
RAROC=Risk-adjusted returnEconomic capitalRAROC = \dfrac{\text{Risk-adjusted return}}{\text{Economic capital}}
numerator = return net of EL and funding costs, denominator = economic capital allocated
Fama-French three-factor model
E[Ri]−Rf=βi,M(RM−Rf)+βi,SMB⋅SMB+βi,HML⋅HMLE[R_i] - R_f = \beta_{i,M}(R_M - R_f) + \beta_{i,SMB}\cdot SMB + \beta_{i,HML}\cdot HML
RMR_M = market return, SMB = small minus big, HML = high minus low book-to-market
APT multifactor expected return
E[Ri]=Rf+βi,1λ1+βi,2λ2+⋯+βi,kλkE[R_i] = R_f + \beta_{i,1}\lambda_1 + \beta_{i,2}\lambda_2 + \cdots + \beta_{i,k}\lambda_k
RfR_f = risk-free rate, βi,kβ_{i,k} = asset i loading on factor k, λkλ_k = factor k risk premium
Treynor ratio
T=Rp−RfβpT = \dfrac{R_p - R_f}{\beta_p}, excess return per unit of systematic risk (beta). Preferred over the Sharpe ratio for ranking well-diversified sub-portfolios where idiosyncratic risk is already diversified away.
Quantitative Analysis 25 items
AR(1) mean-reverting level
μ=α1−ϕ\mu = \dfrac{\alpha}{1 - \phi}
α = intercept, φ = AR(1) coefficient with |φ| < 1, μ = unconditional long-run mean
Continuously compounded (log) return
r=ln⁡(Pt/Pt−1)=ln⁡(1+R)r = \ln(P_t / P_{t-1}) = \ln(1 + R)
PtP_t = price at time t, Pt−1P_{t-1} = prior price, R = simple return over the period
Sample variance with Bessel's correction
s2=1n−1∑i=1n(Xi−Xˉ)2s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})^2
XiX_i = observation i, Xˉ\bar{X} = sample mean, n = sample size
Bayes' rule
P(A∣B)=P(B∣A) P(A)P(B)P(A \mid B) = \dfrac{P(B \mid A) \, P(A)}{P(B)}; P(A) = prior, P(B|A) = likelihood, P(B) = marginal evidence = P(B|A)P(A) + P(B|Aᶜ)P(Aᶜ)
Expected value of a lognormal random variable
E[X]=eμ+σ2/2E[X] = e^{\mu + \sigma^2/2}
μ = mean of ln(X), σ² = variance of ln(X); the σ²/2 is the convexity adjustment
F1 score for binary classification
F1=2⋅P⋅RP+RF_1 = \frac{2 \cdot P \cdot R}{P + R}
P = precision = TP/(TP+FP), R = recall = TP/(TP+FN), TP/FP/FN from confusion matrix
Law of total probability (two-event partition)
P(B)=P(B∣A)P(A)+P(B∣Ac)P(Ac)P(B) = P(B \mid A) P(A) + P(B \mid A^c) P(A^c)
A and A^c partition the sample space, P(B|·) = conditional probability of B
Adjusted R-squared
Rˉ2=1−(1−R2)⋅n−1n−k−1\bar{R}^2 = 1 - (1 - R^2) \cdot \frac{n - 1}{n - k - 1}
R² = unadjusted R-squared, n = sample size, k = number of regressors
OLS slope estimator (single regressor)
β^1=Cov(X,Y)Var(X)\hat{\beta}_1 = \frac{\text{Cov}(X, Y)}{\text{Var}(X)}
Cov(X,Y) = sample covariance of X and Y, Var(X) = sample variance of X
AR(1) h-step-ahead forecast
E[Yt+h]=μ+ϕh(Yt−μ)E[Y_{t+h}] = \mu + \phi^h (Y_t - \mu)
μ = mean-reverting level, φ = AR coefficient, h = forecast horizon, YtY_t = current value
Pearson correlation coefficient
ρX,Y=Cov(X,Y)σXσY\rho_{X,Y} = \dfrac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y}
Cov = covariance of X and Y; σXσ_X, σYσ_Y = standard deviations; ρ ∈ [-1, 1]
Square-root-of-time volatility scaling
σT=σ1T\sigma_T = \sigma_1 \sqrt{T}
σTσ_T = T-period volatility, σ1σ_1 = one-period volatility, T = number of periods (assumes iid returns)
Variance of a linear transformation
Var(aX+b)=a2 Var(X)\text{Var}(aX + b) = a^2 \, \text{Var}(X)
X = random variable, a = scale factor, b = shift constant
Omitted variable bias in a short regression coefficient
bias(β^1)=β2⋅δ\text{bias}(\hat{\beta}_1) = \beta_2 \cdot \delta
β₂ = true coefficient on omitted X₂, δ = slope from regressing X₂ on included X₁
Variance of a two-asset weighted sum
Var(aX+bY)=a2σX2+b2σY2+2ab Cov(X,Y)\text{Var}(aX + bY) = a^2 \sigma_X^2 + b^2 \sigma_Y^2 + 2ab\,\text{Cov}(X,Y)
a, b = weights; σ = standard deviation; Cov = covariance
Variance inflation factor for regressor j
VIFj=11−Rj2\text{VIF}_j = \frac{1}{1 - R_j^2}
R²_j = R-squared from regressing XjX_j on the other regressors; VIF > 10 commonly flags collinearity
One-sample t-statistic for testing a mean
t=Xˉ−μ0s/nt = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}
Xˉ\bar{X} = sample mean, μ0\mu_0 = hypothesized mean, s = sample std dev, n = sample size
Box-Pierce Q-statistic for residual autocorrelation
QBP=T∑k=1mρ^k2Q_{BP} = T \sum_{k=1}^{m} \hat{\rho}_k^2
T = sample size, m = number of lags tested, ρ̂_k = sample autocorrelation of residuals at lag k
LASSO regression penalized objective
min⁡β∑i(yi−y^i)2+λ∑j∣βj∣\min_\beta \sum_i (y_i - \hat{y}_i)^2 + \lambda \sum_j |\beta_j|
yiy_i = observed, ŷ_i = predicted, βjβ_j = coefficient j, λ = L1 penalty strength
Ridge regression penalized objective
min⁡β∑i(yi−y^i)2+λ∑jβj2\min_\beta \sum_i (y_i - \hat{y}_i)^2 + \lambda \sum_j \beta_j^2
yiy_i = observed, ŷ_i = predicted, βjβ_j = coefficient j, λ = L2 penalty strength
Two-sample t-statistic for difference of means
For independent samples, testing equal population means: t=Xˉ1−Xˉ2s12/n1+s22/n2t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{s_1^2/n_1 + s_2^2/n_2}}
Xˉi\bar{X}_i = sample mean i, sis_i = sample std dev i, nin_i = sample size i
Jarque-Bera test statistic
JB=n6[S2+(K−3)24]JB = \frac{n}{6}\left[S^2 + \frac{(K-3)^2}{4}\right]
n = sample size, S = sample skewness, K = sample kurtosis; chi-square with 2 dof under normality
F-statistic for joint hypothesis test
F=(RSSR−RSSU)/qRSSU/(n−k−1)F = \frac{(\text{RSS}_R - \text{RSS}_U) / q}{\text{RSS}_U / (n - k - 1)}
RSSRRSS_R = restricted RSS, RSSURSS_U = unrestricted RSS, q = restrictions, n = sample, k = regressors
Random walk with known drift: h-step conditional forecast and forecast-error variance
Et[Yt+h]=Yt+hd,Vt=hσ2E_t[Y_{t+h}]=Y_t+hd,\quad V_t=h\sigma^2. Model: ΔYt=d+εt\Delta Y_t=d+\varepsilon_t, known drift dd, iid zero-mean innovations with variance σ2\sigma^2. VtV_t is forecast-error variance; standard deviation is σh\sigma\sqrt h. Excludes parameter uncertainty.
Monte Carlo standard error of an estimated mean from independent finite-variance draws
SE^(Xˉ)=sX/N\widehat{SE}(\bar X)=s_X/\sqrt N. sXs_X is output sample SD and NN the iid draw count; finite variance is required. Four times as many draws halves SE. This reduces sampling error, not model bias, and is not the SE formula for a quantile.
Financial Markets and Products 27 items
European call lower bound (no dividend)
c≥max⁡(S0−Ke−rT,  0)c \geq \max(S_0 - K e^{-rT},\; 0)
c = call price, S₀ = spot, K = strike, r = risk-free rate, T = time to maturity
European put lower bound (no dividend)
p≥max⁡(Ke−rT−S0,  0)p \geq \max(K e^{-rT} - S_0,\; 0)
p = put price, K = strike, r = risk-free rate, T = time to maturity, S₀ = spot
Continuous-to-discrete compounding conversion
Rc=mln⁡(1+Rm/m)R_c = m \ln(1 + R_m/m)
RcR_c = continuous rate, RmR_m = rate compounded m times per year, m = compounding frequency
Bull call spread maximum profit
Max profit=K2−K1−D\text{Max profit} = K_2 - K_1 - D
K1K_1 = long (lower) call strike, K2K_2 = short (higher) call strike, D = net debit paid
Optimal number of futures contracts (untailed)
N∗=h∗⋅QA/QFN^* = h^* \cdot Q_A / Q_F
h* = optimal hedge ratio, QAQ_A = size of cash exposure, QFQ_F = futures contract size
Cost-of-carry forward price for a commodity
F0=S0e(r+u−y)TF_0 = S_0 e^{(r+u-y)T}
S₀ = spot, r = risk-free rate, u = storage cost rate, y = convenience yield, T = time to delivery
Forward price on a non-income asset
F0=S0erTF_0 = S_0 e^{rT}
S₀ = spot price, r = continuously compounded risk-free rate, T = time to delivery in years
Relative purchasing power parity
(S1−S0)/S0≈id−if(S_1 - S_0)/S_0 \approx i_d - i_f
S0S_0 = current spot, S1S_1 = future spot, idi_d = domestic inflation, ifi_f = foreign inflation
Put-call parity for European options (no dividend)
c+Ke−rT=p+S0c + K e^{-rT} = p + S_0
c = call price, p = put price, K = strike, r = risk-free rate, T = time to maturity, S₀ = spot price
Long straddle breakeven prices
S∗=K±(c+p)S^* = K \pm (c + p)
K = common strike, c = call premium, p = put premium; profit if |S(T) − K| > c + p
Bond price change with duration and convexity
ΔP/P≈−DmodΔy+12C(Δy)2\Delta P/P \approx -D_{mod} \Delta y + \tfrac{1}{2} C (\Delta y)^2
DmodD_{mod} = modified duration, C = convexity, Δy = yield change
Uncovered interest rate parity expected future spot
E[ST]=S⋅(1+rd)/(1+rf)E[S_T] = S \cdot (1 + r_d) / (1 + r_f)
E[STS_T] = expected future spot, S = current spot, rdr_d = domestic rate, rfr_f = foreign rate
Conditional prepayment rate from single monthly mortality
CPR=1−(1−SMM)12CPR = 1 - (1 - SMM)^{12}
SMM = single monthly mortality, CPR = annualized conditional prepayment rate
Forward price with continuous income yield
F0=S0e(r−q)TF_0 = S_0 e^{(r-q)T}
S₀ = spot, r = risk-free rate, q = continuous income yield (dividend or foreign rate), T = time to delivery
Modified duration from Macaulay duration
Dmod=DMac/(1+y/m)D_{mod} = D_{Mac} / (1 + y/m)
DMacD_{Mac} = Macaulay duration, y = yield, m = compounding periods per year
Cheapest-to-deliver delivery cost
Cost=Quoted price−(F×CF)\text{Cost} = \text{Quoted price} - (F \times CF)
Quoted price = clean bond price, F = futures settlement, CF = conversion factor
Tailed number of futures contracts
Ntailed∗=hRVA/VFN^*_{\text{tailed}} = h_R V_A/V_F
hRh_R uses spot and futures RETURN volatilities; VA=QAS0V_A=Q_A S_0, VF=QFF0V_F=Q_F F_0. Same asset, no income, deterministic carry: hR=1h_R=1, so N∗=(QA/QF)e−rTN^*=(Q_A/Q_F)e^{-rT}. Never pair a price-change ratio with dollar values.
Number of index futures to adjust portfolio beta
N∗=(β∗−β0)⋅P/FN^* = (\beta^* - \beta_0) \cdot P / F
β* = target beta, β0β_0 = current portfolio beta, P = portfolio value, F = index futures contract value
Covered interest rate parity forward rate
F=S⋅(1+rd)/(1+rf)F = S \cdot (1 + r_d) / (1 + r_f)
F = forward rate, S = spot, rdr_d = domestic interest rate, rfr_f = foreign interest rate (matched to horizon)
Duration-based futures hedge ratio
N∗=P⋅DPVF⋅DFN^* = \frac{P \cdot D_P}{V_F \cdot D_F}
P = portfolio value, DPD_P = portfolio duration, VFV_F = futures contract value, DFD_F = CTD bond duration
Swap value to fixed-receiver (two-bond method)
V=Bfix−BflV = B_{\text{fix}} - B_{\text{fl}}
BfixB_{fix} = PV of fixed-rate bond (coupons + notional), BflB_{fl} = PV of floating-rate bond (next coupon + notional)
Fisher relation linking nominal and real rates
(1+r)=(1+ρ)(1+i)(1 + r) = (1 + \rho)(1 + i)
r = nominal rate, ρ = real rate, i = expected inflation
Long forward payoff at maturity
Payoff=ST−K\text{Payoff} = S_T - K
STS_T = spot price at maturity, K = forward strike price
Variance swap payoff at maturity
Payoff=Nvar×(σrealized2−Kvar2)\text{Payoff} = N_{var} \times (\sigma_{realized}^2 - K_{var}^2)
NvarN_{var} = variance notional, σ²_realized = realized variance, KvarK_{var} = strike volatility
Long put option payoff at maturity
Payoff=max⁡(K−ST,0)\text{Payoff} = \max(K - S_T, 0)
K = strike price, STS_T = spot at maturity
FRA settlement payment
Payment=N (rref−rFRA) (d/360)1+rref (d/360)\text{Payment} = \dfrac{N\,(r_{ref} - r_{FRA})\,(d/360)}{1 + r_{ref}\,(d/360)}, settled at the start of the reference period. N = notional, d = day count, rrefr_{ref} = reference rate.
One-period bond expected return: survival pays coupon plus face, default pays recovery only
E[r]=(1−p)(F+C)+pRFP0−1E[r]=\frac{(1-p)(F+C)+pRF}{P_0}-1. P0P_0: price; FF: face; CC: coupon; pp: physical default probability; RR: recovery fraction of face. All cash arrives at period end; default pays no coupon.
Valuation and Risk Models 26 items
Forward rate between two dates (continuous compounding)
f(t1,t2)=s2t2−s1t1t2−t1f(t_1, t_2) = \frac{s_2 t_2 - s_1 t_1}{t_2 - t_1}
s1, s2 = spot rates to t1 and t2, f = forward rate from t1 to t2
Black-Scholes-Merton call price (no dividends)
C=S0N(d1)−Ke−rTN(d2)C = S_0 N(d_1) - K e^{-rT} N(d_2)
S₀ = spot, K = strike, r = risk-free rate, T = maturity, N = standard normal CDF
Cox-Ross-Rubinstein up and down factors
u=eσΔt, d=1/uu = e^{\sigma \sqrt{\Delta t}},\ d = 1/u
σ = annualized volatility of the underlying, Δt = step length in years
BSM gamma for a European option (no dividends)
Γ=ϕ(d1)/(S0σT)\Gamma = \phi(d_1) / (S_0 \sigma \sqrt{T})
φ = standard normal density, S₀ = spot, σ = volatility, T = maturity
d₁ in the Black-Scholes-Merton formula (no dividends)
d1=ln⁡(S0/K)+(r+σ2/2)TσTd_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}
S₀ = spot, K = strike, r = rate, σ = volatility, T = maturity
Unexpected loss on a single credit exposure (binomial default)
UL=EAD×LGD×PD(1−PD)UL = EAD \times LGD \times \sqrt{PD(1-PD)}
EAD = exposure at default, LGD = loss given default, PD = probability of default
Risk-neutral probability in a binomial tree
p=erΔt−du−dp = \frac{e^{r \Delta t} - d}{u - d}
r = risk-free rate, Δt = step length, u = up-factor, d = down-factor
Unconditional default probability under constant hazard rate
P(τ≤t)=1−e−λtP(\tau \le t) = 1 - e^{-\lambda t}
λ = constant hazard rate (annual default intensity), t = horizon in years, τ = default time
KR01 from key-rate duration
KR01k=KRDk⋅P⋅10−4\text{KR01}_k = \text{KRD}_k \cdot P \cdot 10^{-4}
KRDkKRD_k = key-rate duration at rate k, P = bond price; dollar change per 1 bp shift
Survival probability under constant hazard rate
P(τ>t)=e−λtP(\tau > t) = e^{-\lambda t}
λ = constant hazard rate, t = horizon in years, τ = default time
Bond price from discount factors
P=∑i=1nc⋅d(ti)+F⋅d(tn)P = \sum_{i=1}^{n} c \cdot d(t_i) + F \cdot d(t_n). P = bond price, F = principal repaid at maturity, c = each coupon payment, d(t) = discount factor for time t, n = number of payments.
Basel total market-risk capital with stressed VaR
K=max⁡(VaRt−1,mcVaR‾)+max⁡(sVaRlatest,mssVaR‾)K=\max(VaR_{t-1},m_c\overline{VaR})+\max(sVaR_{latest},m_s\overline{sVaR}). Basel 2.5 VaR plus stressed-VaR charge: bars are 60-business-day means; supervisory multipliers mc,ms≥3m_c,m_s\ge3, with backtesting adjustments. Other applicable market-risk charges are additional.
Expected Shortfall under normal returns
ESc=−μ+σϕ(zc)1−c\text{ES}_c=-\mu+\sigma\frac{\phi(z_c)}{1-c}
μ\mu and σ\sigma describe returns; loss is minus return. Multiply by portfolio value for dollar ES. zc=Φ−1(c)z_c=\Phi^{-1}(c); ϕ\phi is standard-normal density.
Effective duration from shocked prices
Deff=P−−P+2P0ΔyD_{\text{eff}} = \frac{P_- - P_+}{2 P_0 \Delta y}
P₋ = price after yield drop, P₊ = price after yield rise, P₀ = base price, Δy = shock size
Parametric (delta-normal) VaR
VaRc=−μ+zcσ\text{VaR}_c = -\mu + z_c \sigma
μ = expected return, σ = return standard deviation, zcz_c = one-sided standard-normal quantile at confidence c
Loss given default from recovery rate
LGD=1−RR\text{LGD} = 1 - \text{RR}
LGD = loss given default (fraction of exposure lost), RR = recovery rate (fraction of par recovered after default)
Macaulay duration
Dmac=∑i=1nti⋅PV(Ci)PD_{\text{mac}} = \sum_{i=1}^{n} t_i \cdot \frac{PV(C_i)}{P}
tit_i = time to cash flow i, PV(C_i) = present value of cash flow i, P = bond price
Effective annual rate from nominal rate
EAR=(1+r/n)n−1\text{EAR} = (1 + r/n)^n - 1
r = nominal annual rate, n = compounding periods per year
Dollar value of an 01 (DV01)
DV01≈Dmod×P×10−4\text{DV01} \approx D_{\text{mod}} \times P \times 10^{-4}
DmodD_{mod} = modified duration, P = bond price; dollar price change for a 1 bp yield change
GARCH(1,1) variance recursion
σt2=ω+αrt−12+βσt−12\sigma_t^2 = \omega + \alpha r_{t-1}^2 + \beta \sigma_{t-1}^2
ω = constant, α = ARCH weight on lagged squared return, β = GARCH weight on lagged variance
Conditional one-year default probability given survival
P(default in next year∣survived)=1−e−λP(\text{default in next year} \mid \text{survived}) = 1 - e^{-\lambda}
λ = constant annual hazard rate; value is the same each year under constant intensity
Vasicek single-factor credit VaR (Basel IRB)
dc=Φ((Φ−1(PD)+ρΦ−1(c))/1−ρ)d_c=\Phi((\Phi^{-1}(PD)+\sqrt{\rho}\Phi^{-1}(c))/\sqrt{1-\rho}). This is the limiting default fraction. Total-loss VaR is EAD×LGD×dcEAD\times LGD\times d_c; capital is EAD×LGD×(dc−PD)EAD\times LGD\times(d_c-PD) if EL is covered separately. IRB adds regulatory specifications.
Option vega
ν=∂V/∂σ\nu=\partial V/\partial\sigma uses decimal volatility. A one-percentage-point rise has Δσ=0.01\Delta\sigma=0.01, so ΔV≈0.01ν\Delta V\approx0.01\nu: raw vega 27.58185 equals 0.2758185 per percentage point. Long vanilla calls and puts have positive vega, generally larger near the money and at longer maturities.
Standardized operational risk capital from BIC and the applicable loss multiplier
Kop=BIC×ILMK_{op}=BIC\times ILM. BICBIC: business indicator component from marginal BI coefficients; ILMILM: internal loss multiplier. Normally ILM=1ILM=1 in bucket 1; national discretion may use losses there or set it to 1 for all banks. BI alone is not capital.
Price of a fixed-rate bond from its nominal annual yield with m coupons per year
P=∑j=1nC/m(1+y/m)j+F(1+y/m)nP=\sum_{j=1}^{n}\frac{C/m}{(1+y/m)^j}+\frac{F}{(1+y/m)^n}. CC: annual coupon amount; FF: face; yy: nominal annual YTM; mm: payments/year; nn: remaining periods. Price just after a coupon; fixed promised cash flows, periodic compounding.
Bond holding-period return including coupon reinvestment to the horizon
HPR=PH+FVH(C)−P0P0HPR=\frac{P_H+FV_H(C)-P_0}{P_0}. P0,PHP_0,P_H: full purchase and horizon sale/redemption prices; FVH(C)FV_H(C): coupons accumulated to the horizon including reinvestment. Do not double-count terminal coupons. This is the whole-period return before costs and tax.
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The full original question bank is free with an account, subject to usage limits. Worked solutions, written lessons, mixed practice, and your readiness score stay free. The formula sheet is free too. Fellow is $39 per month or $79 per quarter, per exam family (USD). Fellow Plus is $49 per month, $99 per quarter, or $199 per year, per exam family (USD). Every annual plan is Fellow Plus. Fellow adds timed mock exams, spaced-repetition flashcards, performance analytics, and a personalized study plan.

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Exam P Exam FM Exam FAM Exam SRM Exam PA Exam ALTAM Exam ASTAM CFA Level I CFA Level II CFA L3 Portfolio Mgmt CFA L3 Private Wealth CFA L3 Private Markets

About FreeFellow

Jeffrey Ting, founder of FreeFellow
Jeffrey Ting
FSA, CFA · Founder

FreeFellow was built by Jeffrey Ting, a credentialed actuary and CFA charterholder who has passed thirteen of the hardest exams in finance, all on his first attempt. He paid four-figure prep fees along the way.

So he started writing his own questions, then lessons, then mock exams, until it grew into a full prep platform covering 41 exams with more than 48,000 original practice questions.

01
Cost shouldn't decide who gets in.

A CFA charter, a CPA license, an actuarial credential. Each opens a real career, but prep fees add to the cost of getting there. FreeFellow keeps its original question bank and written lessons free so you can study even if a paid course is out of reach.

02
Free should mean free.

The original question bank, the worked solutions, the topic lessons, mixed practice, and your readiness score stay free, forever. Full access needs a free account, and practice usage limits apply. Fellow adds AI grading on supported exams, spaced-repetition flashcards, full-length mock exams, analytics, and a study plan that adapts to your progress.

Meet the founder ›Read the values ›

Free forever

Put the formulas to work.

Every formula on this sheet shows up in the free FRM Part I question bank, and every question carries a step-by-step solution.

Practice FRM Part I questions free →

No credit card. No trial clock.