FRM Exam: Essential BA II Plus Functions You Must Know
The FRM leans on the statistics worksheet rather than the TVM row: regression for beta, root-252 for volatility, LN for log returns, numerical duration.
The short answer
The FRM uses a different half of the BA II Plus than the CFA does. The keys that matter are the two-variable statistics worksheet in LIN mode, which returns the intercept a, the slope b and the correlation r for a beta or hedge-ratio question; the square-root key for scaling volatility across time; and LN and e^x for continuously compounded returns. Duration and convexity are not registers on the standard model, but both come out of two extra BOND computations. The TVM row still matters, it just carries less of the exam.
Candidates arriving at the FRM from the CFA usually bring the wrong half of the calculator with them. The CFA is a valuation exam and it lives in the TVM row. The FRM is a risk exam, and risk is dispersion — so it lives in the statistics worksheet, the square-root key and the natural log.
The TVM row still earns its place. It just carries a much smaller share of the paper than you are used to, and the functions that replace it are the ones most candidates have never opened.
What the FRM actually asks the calculator to do
| Topic | The keys |
|---|---|
| Volatility of a return series | 2ND DATA, 2ND STAT — read Sx |
| Annualising or scaling volatility | √ and × |
| Beta, hedge ratio, factor loading | 2ND STAT in LIN mode — read b |
| Correlation and covariance | r, then r × Sx × Sy |
| Parametric VaR and expected shortfall | one multiplication each |
| EWMA and GARCH volatility updates | x², STO, RCL |
| Continuously compounded returns | LN and e^x |
| Bond price and yield | 2ND BOND |
| Duration and convexity | two extra BOND computations |
| Expected loss, discounted exposure | CF and NPV |
GARP’s approved calculator list has historically been wider than the CFA’s — the BA II Plus and Professional, the HP 12C family and the HP 10B II family — but the list is GARP’s to change, so confirm it on their site rather than trusting this page.
The regression worksheet is the FRM function
If you learn one worksheet for this exam, learn this one. Two-variable statistics in LIN mode returns a
slope, an intercept and a correlation coefficient from paired data, which covers beta, hedge ratios,
factor loadings and every “estimate the relationship” item on the paper.
Six months of returns: a benchmark index, and a stock you are estimating beta for.
| Month | Index (X) | Stock (Y) |
|---|---|---|
| 1 | 2.1 | 4.6 |
| 2 | −1.4 | −1.2 |
| 3 | 3.6 | 4.9 |
| 4 | 0.8 | 1.1 |
| 5 | −2.3 | −5.3 |
| 6 | 4.2 | 7.9 |
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2ND -
DATA -
2ND -
CLR WORK -
2.1 -
ENTER -
↓ -
4.6 -
ENTER -
↓ -
1.4 -
+|− -
ENTER -
↓ -
1.2 -
+|− -
ENTER -
↓ -
… -
4.2 -
ENTER -
↓ -
7.9 -
ENTER -
2ND -
STAT
If 2ND STAT does not show LIN, press 2ND SET until it does. The Ln, EXP and PWR models fit the same data to curves and will quietly give you a different slope.
| Register | Value | What it is |
|---|---|---|
n |
6 | Pairs entered — check first |
X̄ |
1.1667 | Mean index return |
Sx |
2.6357 | Index volatility, sample |
Ȳ |
2.0000 | Mean stock return |
Sy |
4.7816 | Stock volatility, sample |
a |
−0.0567 | Intercept — alpha, in this framing |
b |
1.7629 | Slope — beta |
r |
0.9717 | Correlation coefficient |
Two numbers you will be asked for and will not find on the display:
-
R² = r × r = 0.9717²= 0.9442 Cov(X,Y) = r × Sx × Sy = 0.9717 × 2.6357 × 4.7816 ≈ 12.2460
There is no covariance register on either model. The identity is on the formula sheet and it is two keystrokes here.
So the stock has a beta of 1.76 against this index, 94.4% of its variance is explained by the index, and the covariance is 12.2460 in percent-squared units.
Scaling volatility: the √ key does most of the work
Risk is quoted at whatever horizon the question wants, and moving between horizons is the square-root-of- time rule.
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σ over T periods = σ per period × √T
Only valid when returns are independent and identically distributed — which is the assumption the exam is testing, not a fact about markets.
| Horizon | Multiplier | Volatility |
|---|---|---|
| 1 day | 1 | 1.2000% |
| 10 days | √10 = 3.1623 | 3.7947% |
| 1 month (21 days) | √21 = 4.5826 | 5.4991% |
| 1 year (252 days) | √252 = 15.8745 | 19.0494% |
Two hundred and fifty-two is the convention for trading days and the number the FRM uses unless the question says otherwise. Note what the rule does not say: it does not scale returns, which grow linearly, only volatility, which grows with the square root. Getting those two the wrong way round is a standard distractor.
VaR and expected shortfall are multiplications
Neither has a function, and neither needs one.
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VaR = position × z × σ ES = position × σ × φ(z) ÷ (1 − c)
z is 1.645 at 95% and 2.326 at 99%. φ is the standard normal density at z, which the exam supplies or you compute with e^x.
A £10m position with a 1.2% daily volatility.
| Measure | Working | Result |
|---|---|---|
| 1-day 95% VaR | 10,000,000 × 1.645 × 0.012 | £197,400 |
| 10-day 95% VaR | 197,400 × √10 | £624,234 |
| 1-day 99% VaR | 10,000,000 × 2.326 × 0.012 | £279,120 |
| 1-day 95% expected shortfall | 10,000,000 × 0.012 × 2.0622 | £247,466 |
The expected shortfall multiplier is φ(1.645) ÷ 0.05 = 0.103111 ÷ 0.05 = 2.0622, against a VaR multiplier of 1.645. Expected shortfall is always the larger, because it averages the tail rather than cutting it off, and the ratio 2.0622 ÷ 1.645 = 1.2536 is worth memorising as a sanity check at 95%.
EWMA in one line, and why STO matters
The exponentially weighted update is arithmetic, but it is arithmetic you may have to run several times on one item.
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σ²ₙ = λ σ²ₙ₋₁ + (1 − λ) r²ₙ₋₁
Work in variance, not volatility. Square first, update, then take the root at the end — squaring and rooting on every step is where the errors come in.
Yesterday’s volatility estimate was 1.2%; today’s return was 2.3%. λ = 0.94.
-
0.012 -
x² -
× -
0.94 -
= -
STO -
1 -
… -
0.023 -
x² -
× -
0.06 -
= -
+ -
RCL -
1 -
= -
√
New volatility = 1.2927%. A 2.3% shock — nearly twice the prevailing volatility — moves the estimate by less than a tenth of a percentage point, which is the point of λ = 0.94 and a common conceptual question. Store the variance rather than the volatility if the item asks for two consecutive updates.
Continuous compounding: LN and e^x
The FRM uses continuously compounded returns far more than the CFA does, because they are additive across time. Two conversions cover almost everything.
| Question | Keys | Result |
|---|---|---|
| Continuous rate equivalent to 6% effective | 1.06 LN |
5.826891% |
| Effective rate equivalent to 6% continuous | 0.06 e^x then − 1 |
6.183655% |
| Log return when a price goes 100 → 105 | 1.05 LN |
4.8790% |
| Price after a 6% continuous return | 0.06 e^x then × 100 |
106.1837 |
The 6% pair is worth holding in memory as an anchor: 6% continuous is 6.183655% effective, and 6% effective is 5.826891% continuous. Continuous is always the smaller number for the same growth, and if your answer is the other way round you have used the wrong key.
The ICONV worksheet handles discrete frequencies — 6% nominal is 6.09% effective semiannually and
6.167781% monthly — but it has no continuous setting, so LN and e^x are the route. The interest
conversion calculator runs the whole progression, continuous compounding
included.
Duration is not enough: adding convexity
Neither duration nor convexity is a register on the standard BA II Plus, and both are two BOND
computations away. Price the bond either side of its yield and read the slope and the curvature.
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ModD ≈ (P₋ − P₊) ÷ (2 P₀ Δy) Convexity ≈ (P₋ + P₊ − 2P₀) ÷ (P₀ Δy²)
Δy of 25 basis points is a good compromise: small enough to be local, large enough that rounding in PRI does not dominate.
The 4.5% of February 2034 at a 5.25% yield: P₋ = 96.9047 at 5.00%, P₀ = 95.3994, P₊ = 93.9217 at 5.50%.
ModD = 6.2537 and convexity = 46.16. Now the reason the FRM insists on the second term:
| Yield move | Duration only | Duration + convexity | Actual | Error with convexity |
|---|---|---|---|---|
| +100 bp | 89.4334 | 89.6536 | 89.6481 | +0.0055 |
| +200 bp | 83.4674 | 84.3481 | 84.3034 | +0.0447 |
At 200 basis points, duration alone is 0.84 of a point wrong — enough to change a hedge. Adding the convexity term cuts that to 0.04. Every duration-only error is in the same direction, understating the price, because a straight line drawn against a convex curve always falls below it. The bond pricing tutorial has the full error table.
Four settings that break an FRM answer
- The regression model.
LINis one of four.Ln,EXPandPWRfit the same pairs to curves and return a slope that is not a beta. Sxagainstσx. A sample of returns takesSx. The choice moves a VaR figure by several percent and there is an answer choice waiting for the wrong one.- Leftover pairs in
2ND DATA.2ND CLR WORKinside the worksheet. Checknbefore reading anything else. - Day-count basis and coupon frequency in
2ND BOND. Both survive2ND CLR WORKvisibly only if you arrow onto them, and both change a duration estimate.
What to drill
| Task | Target |
|---|---|
Sx from eight returns |
45 s |
| Annualise a daily volatility | 10 s |
| Beta and r from six pairs | 70 s |
Covariance from r, Sx, Sy |
10 s |
| VaR at two confidence levels | 20 s |
| One EWMA update | 25 s |
| Numerical duration from three prices | 90 s |
The regression row is the one to time yourself on, because it is the longest sequence on the paper and the one candidates have practised least. Seventy seconds of keying for a question worth the same as a ten-second one is a poor trade, which is exactly why it is worth getting fast at.
If the keypad itself is still unfamiliar, how to use the BA II Plus covers the layout and the four different clears, and CFA exam calculator tips shares most of the setup discipline — the settings that ruin an answer are the same on both exams.