There are a ton of formulas you need to know for the Level 2 exam.
For me, as with others, it is the most quantitatively intensive test I’ve ever taken.
But do you really need all those formulas, and how do you memorize so much in such a quick time?
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Most important CFA Level 2 formulas
In this post we’ll look at the most important formulas in the second exam and how to approach the massive amount of material.
The usual disclaimer applies, while I have been writing on the exams for quite a while and took them myself, no one knows what will actually show up on the exam. All the curriculum is testable.
I can only tell you what I have seen through my own experience and what I have seen on successive versions of the curriculum over the last four years.
We’ll start with a general approach to the formulas then look at each study session to pick out the most important formulas.
Remembering every single calculation from the curriculum is not practical for most candidates and it does seem that the Institute targets some material as more important than others.
That said, it is extremely easy to get into the punter’s trap. I call the punter’s trap where you find a tough formula and decide to skip it and focus on easier points instead.
Something like punting in football instead of going for the extra yardage.
The problem is, once you start doing this it gets easier to do it again and again.
Pretty soon, you are skipping a good portion of the curriculum and you are guaranteed some lost points on the exam. Spend the time and get these formulas down.
There’s two things you can do to help get through the tough formulas.
- First, you need to understand what is conceptually happening in the formula. Trying to understand the myriad of symbols is crazy. If WACC = (Vd/(Vd +Vce))rd (1-t) + (Vce/(Vd+Vce))rce) doesn’t make you go cross-eyed you are a stronger person than I am.
Think about it intuitively and it makes sense. The overall cost of a firm’s funding capital is the cost and proportion of equity and debt.
The percentage of each funding type relative to the total is multiplied by its cost. Debt is tax advantaged, so you need the after-tax cost.
- Secondly, you have to work these formulas through practice and repetition. One of the most popular posts here shows that active learning (engaging CFA study material through practice and conversation) allows you to remember much more than passive learning.
The best way to approach tough formulas is to put them on flash cards. Write out a full practice question like those at the end of the chapters. Then work the questions each day. When you are able to do one easily, put it aside so the time necessary each day decreases. You will want to review them all every couple of weeks to make sure you haven’t forgotten any.
We’ll go through each study session to look at the high level important questions but make sure you are doing the end-of-chapter and blue-box questions in the curriculum.
If the Institute is taking the time to write out a problem, then they want you to know the formula and you could see it on the exam.
There are no calculations in the first two study sessions, just ethics material but this is extremely important to your overall grade so you may want to review our posts on ethics and standards.
You need to know how to calculate the sample covariance and correlation coefficient.
Learn the basics of the formula but you can do both of these on your calculator so learn how to input the data and you’ll save a lot of time.
You need to know how to calculate a value for a regression model, which is pretty easy by just plugging the numbers into the variables in the formula.
The correlation coefficient is just the covariance divided by the standard deviations of each variable.
Ryx = COVyx/sysxwith the covariance being the sum of the differences (y- average y)(x – average x) divided by the sample size minus one.
Remember, the slope estimate (b1) is the covariance divided by the variance.
What gets most candidates is the various statistics on the ANOVA chart so learn the parts and be able to interpret their meaning.
Predicting the value of a time series or the autoregressive model is similar to the regression model, just plug in the numbers.
Be sure you can work a formula with a seasonal lag as well. You may also need to calculate a mean reverting level.
Forex can be tough, especially with the confusion around direct and indirect quotes.
You need to be able to calculate the bid-ask spread as well as calculate the profit on a triangular arbitrage.
I have included two video explanations to get you started.
A good explanation of Bid and Ask quotes is available on YouTube at:
Cross rates and arbitrage are easily testable and will really test whether you understand forex quotes and calculations. A good explanation of triangular arbitrage is available on YouTube at:
The forward premium or discount on a currency is just the relative difference between the forward and spot price (Fxy – Sxy)/ Sxy multiplied by the annualized time in the contract (12/# of months until settlement)
Interest rate parity is an important concept and the formula is fairly easy. It’s just the relative interest rates (1+rx/1+ry) times the spot price.
FRA Intercorporate Investments, Post-Employment and Share-based Compensation, and Multinational Operations
Most of the FRA material is more knowing the accounting and procedures rather than complex formulas.
Once you know what adjustments or expenses to be made to a beginning entry then the calculations are really little more than addition/subtraction.
The pension material is important here and you’ll see the same accounting in the next exam as well. Be able to calculate the defined benefit pension obligation and the net pension liability or asset.
For the ending DBO = Beginning + Service Cost + Interest Cost +/- Past service cost from current amendments +/- actuarial gains or losses in the current period – benefits paid
Be able to calculate the pension expense and economic pension expense as well.
The translation effects on the balance sheet and income statement through the temporal and current rate methods is something that has been in the curriculum for a while and often appears on the exam.
Remember, the gains and losses from the use of the temporal method go directly to the income statement whereas the gains/losses from the current rate method go to the CTA in the stockholders’ equity section of the balance sheet.
The balancing ‘plug’ number for the current rate method is the cumulative translation adjustment while the plug number for the temporal method is retained earnings and the gain from translation on the income statement.
Economic profit is a fairly important formula here with the other formulas (i.e. market value added, residual income) also easily testable and seen in other sections of the exam.
Economic profit is the excess earned over the dollar cost of capital invested.
- EP = NOPAT – SWACC
- NOPAT = Net operating profit after tax, EBIT (1-tax rate)
- SWACC = dollar cost of capital, WACC* Capital
- Market Value Added (MVA) is the NPV calculation of Economic Profit
Be able to calculate dividends under three dividend policies: Stable, constant dividend payout ratio, and residual.
- Under the stable dividend policy, a payout is set for long term and the target payout ratio is used to find the expected increase. The expected increase is the increase in earnings times the target ratio times an adjustment factor (the reciprocal of the number of years to adjust the dividend)
- Under the constant payout ratio policy, the dividend fluctuates with net income and may be volatile.
- Under the residual policy, dividends = earnings – (capital budget*equity % in capital structure)
Corporate Finance: Financing and Control
The post-merger EPS is the acquirer’s pre-merger earnings plus the target’s pre-merger earnings divided by the post-merger shares outstanding.
Remember that the acquirer may have to issue new shares equal to the target’s market cap divided by the acquirer’s stock price.
The Herfindahl-Hirshman Index is something that comes up frequently but really isn’t too difficult.
Just take each firm’s market share times 100 and then squared, then add them all up. Realistic numbers are usually above 500 up to 3,000 so make sure you check your answer.
You’ll need to remember the three levels of concentration and the likelihood of an antitrust challenge (i.e. < 1,000, 1,000- 1,800, >1,800)
You may need to calculate the free cash flows for a target company through NOPLAT. NOPLAT is the unlevered net income plus any change in deferred taxes.
FCF = NOPLAT + Noncash charges – changes in net working capital – capex.
Don’t forget to discount the FCF to a present value using the appropriate rate.
The weighted average cost of capital is a fairly easy calculation but can cost you points if you rush through it.
Don’t forget to use the after tax cost of debt, rate (1-tax rate).
It is usually preferred to use the target weights for capital structure rather than the current market value weights when finding WACC.
Industry and Company Analysis
There are some extremely important and testable formulas in this reading. You should be able to work the dividend discount model solving for any one of the variables in case they ask for the discount rate or the dividend growth rate.
Remember, the Gordon growth model is a DDM under the constant growth assumption while the H-model or the multi-stage models assume different growth rates.
Under the Gordon growth, value = (current dividend * (1+growth rate)) divided by the required rate minus growth
The H-model is taking a basic DDM (initial dividend rate divided by rate minus long-term growth) but multiplies in a bonus because of supernormal growth (the difference in rates times half the years plus the long-term growth rate).
The second part of the equation is a mathematical attempt at estimating a linear (straight line) decline in growth.
Be able to decompose the return on equity in a DuPont Analysis down to its most basic pieces.
ROE = NI/Sales * Sales/Total Assets * Total Assets/Shareholders’ Equity
If you forget, just remember that ROE is NI/Equity so all the other variables must cancel out (i.e. sales is denominator in NI/Sales and numerator in Sales/Assets). Remember that these are also net profit margin * asset turnover* leverage.
Free cash flow is an extremely important measurement and you will need it extensively in the equity section of the exam, especially at level II.
It represents the cash available to either equity investors or all capital providers after all working capital and fixed capital needs have been accountable.
Basically, it is the extra cash available to owners (of debt or equity) after the company’s future operations have been funded.
Free Cash Flow to the Firm (FCFF) is the cash flow available to all capital providers (debt and equity) and equals:
Net income + Net noncash Charges (depreciation and amortization) – Investment in working capital – Investment in Fixed capital + after tax interest expense
Free Cash Flow to Equity (FCFE) is the cash flow available to common shareholders and equals:
Net income + Net noncash Charges (depreciation and amortization) – Investment in working capital – Investment in Fixed +/- net borrowing
- Notice that FCFE is FCFF except without adding back interest expense and taking net borrowing into account.
- Understand how to arrive at FCFE or FCFF with CFO
- FCFF = CFO + INT (1-t) – invest fixed capital
- FCFE= CFO – invest fixed capital +/- net borrowing
Be able to understand and calculate price multiples like price/earnings, price/book, price/sales, and price/earnings to growth on a trailing and forward basis.
Enterprise value multiples like EV/EBITDA or EV/Sales are important along with the other price multiples.
Remember, Enterprise Value is market value equity + market value preferred + market value debt – cash & investments.
In its most basic form residual income is net income minus an equity charge or just the income remaining after a theoretical cost of the equity used.
Net Income – (equity capital*cost of equity)
You may see the calculation including NOPAT which is Net Income + the after tax interest expense so be ready for RI = NOPAT- (WACC*Total Capital) as well.
The valuation model using residual income and book value can be lengthy but is absolutely necessary to learn.
Go through a couple of examples until you are sure you have it down for the test.
The Learning outcome statements say you need to be able to calculate the value of real estate over all three approaches; income, cost and sales but the focus of the curriculum is clearly on the income approach and understanding net operating income (NOI).
The cost and sales approach to valuation are fairly simple. Cost is just the total expense of creating a similar property while the sales approach looks at the square foot value of similar properties that have sold on the open market.
Of the three valuation methods using income, the direct capitalization is the most important though you also need to understand the DCF and multiplier methods.
The discounted cash flows method is just like any other DCF where you take the cash flows over the life of the investment along with a terminal value and discount them to a present value.
The multiplier method involves multiplying the gross income from a property by a multiple derived from sales data on similar properties.
The direct capitalization approach revolves around finding the net operating income (NOI) and a cap rate which is the rate of return required by investors.
Gross rental income minus vacancy or collection losses is the effective gross income.
The effective gross minus (utilities, taxes, insurance, maintenance, management and advertising) equals the NOI.
* Remember –financing costs and federal income taxes are not subtracted for NOI because the value is independent of financing and is a before-tax, unleveraged measure of income. Depreciation is also not removed.
The cap rate will usually be given or you will need to calculate it from sales and NOI data from similar properties.
Otherwise, the cap rate can be found by (discount rate minus growth rate) as well.
The property value is then NOI/cap rate.
Understand how to arrive at the NAV of a REIT and calculate the NAV per share as well as the concept of Funds from Operation (FFO) and REIT price multiples.
Understand the difference between FFO and bottom-line earnings and why FFO is a better metric for REITs.
NAV per share = (market value of real estate company’s assets – market value of company’s liabilities)/number of shares outstanding.
The private equity section is testable as well with formulas for distributed to paid in (DPI), residual value to paid in (RVPI), and total value to paid in (TVPI).
You also need to know the pre-money and post-money valuation as well as the ownership fraction and price per share in venture capital financing.
DPI= sum of distributions/ cumulative capital called down
RVPI = NAV after distributions/ cumulative capital called down
TVPI (also called the investment multiple) is = DPI + RVPI
Fixed Income Valuation Concepts
Be sure to understand all the financial ratios in credit analysis like: operating profit margin, debt/EBITDA, EBIT or EBITDA to interest expense, and debt/capital.
Understand that the impact on return may be different for small and large yield changes.
The impact on return for small, instantaneous changes is (-modified duration)* the change in the spread,
while the impact for a large change in yield is (-modified duration*spread change) plus ½ convexity * (change in spread squared).
You may also need to value a callable or putable bond using an interest rate tree.
Constructing a binomial interest rate tree.
1) Given the coupon rate and maturity, use the yield on the current 1-year on-the-run issue for today’s rate.
2) Assume the level of rate volatility
3) Given the coupon rate and market value of the 2-year on-the-run issue, select a value of the lower rate and compute the upper rate. R1,u= r1,l * e2volatility
R1,u is the upper rate (1 reflects the interest rate starting in year 1 and u reflects the higher of the two rates in year 1)
Volatility is the assumed volatility of the 1-period rate
e is the natural antilogarithm, 2.71828
4) Compute the bond’s value one year from now using the interest rate tree
5) If the value calculated using the model is greater than the market price, use the higher rate of r1,l and recomputed r1,u and then calculate the new value of the on-the-run issue using new rates. If the value is too low, decrease the interest rates in the tree.
6) The five steps are repeated with a different value for the lower rate until the value estimated by the model is equal to the market price.
Derivatives: Forwards and Futures
The two study sessions covering derivatives are where the formulas get especially intense. You can’t afford to neglect the material because it is worth between 5% and 15% of your total exam score. Start by understanding the basic concepts behind the formulas to give yourself a chance at an educated guess if you forget the formula itself.
Be able to price equity or fixed-income forward as well as find the value of the contract over its life. Remember, the price of a forward is based on an arbitrage relationship between the contract and the underlying determined by how much it would cost to buy and hold the asset using borrowed funds.
Knowing this means that you need the current price, interest rate, any cash flows in or out, and the contract length to be able to calculate the forward contract.
Forward = (S0 – PV(CF))(1+r)t
You should be able to work through an arbitrage scenario given these data points and the price of a forward contract, first understanding if an arbitrage profit is available then calculating the profit.
Forward rate agreements are also very testable so be able to value a contract. FRA are agreements to pay (or receive) a set interest rate and receive (or pay) a floating rate that is determined at contract expiration.
The payoff on a FRA is = Notational times ( underlying rate at expiration – forward contract rate)(days in underlying rate/360) divided by (1+underlying rate at expiration (days in underlying/360))
It may seem like an intimidating formula but it is really just the difference in rates at expiration multiplied by a time factor relative to the contract length. Make sure you use 360 for the days in a year.
Derivatives: Options, Swaps, and Rate Derivatives
Being able to calculate synthetic positions using options is a matter of knowing the put-call parity formula. The relationship says that the value of a call plus the (strike price divided by (1+risk free rate)t) should be equal to the value of a put and the underlying asset.
C0 + (x/(1+Rf)T) = P0 + S0
Rearranging this formula, you can find the price for synthetic positions by putting C0, P0, or S0 alone on one side of the equation.
Be able to calculate the payment to a cap or floor holder.
Payment to cap is the max of either zero or notational*(index rate – cap strike rate)*(days in settlement period/360)
While the payment to the floor holder is the max of either zero or notational*(floor strike rate – index rate)*(days in settlement period/360)
The swaps material can be lengthy and complicated with formulas for the fixed payment, floating payment and for the pricing. Remember that currency swaps involve two different currencies and the notational principal is usually exchanged at initiation.
Portfolio management becomes the focus on the Level 3 exam, so it really pays to learn CFA study material on the second exam to save time next year. The expected return and standard deviation on a two-asset portfolio is a common question and fairly easy. Remember that the return is just the weighted returns of the assets while you’ll need the variance and correlation coefficient for the standard deviation.
Varianceportfolio = w21*σ21+w22 σ22+ 2w1w2(correlation) σ1 σ2
*Remember to take the square root of the variance to get the standard deviation.
Also be able to calculate the expected return on an asset given factor sensitivities and factor risk premiums, which is basically just a regression-type formula.
The formulas in these three posts should get you started on the list of most likely to show up on the exam. While you cannot take a formula sheet into the test with you, it’s a good idea to write one up just to practice the formulas and commit them to memory.
Joseph Hogue, CFA
FinQuiz offers a complete list of all formulas for Level II.