This is the last of three posts covering the must know formulas for the Level 2 CFA exam. In this post we’ll cover study sessions 13 through 18. The other two posts can be found here: part 1 and part 2.

**SS13- Alternative Investments**

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

**SS14- 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 * e ^{2volatility}**

Where:

**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.

**SS15- Structured Securities**

Be able to calculate the prepayment amount on a passthrough security given a monthly mortality rate. Remember, the

**single monthly mortality (SMM) is the prepayment/(beginning mortgage balance – scheduled principal payment)**

The annualized SMM is the conditional prepayment rate (CPR) and is 1-(1-SMM)

^{12}

**SS16- 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 = (S**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.

_{0}– PV(CF))(1+r)^{t }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.

**SS17- 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)**should be equal to the value of a

^{t})**put**and the

**underlying asset**.

C

_{0}+ (x/(1+R

_{f})

^{T}) = P

_{0}+ S

_{0}

Rearranging this formula, you can find the price for synthetic positions by putting C

_{0}, P

_{0}, or S

_{0}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.

**SS18- Portfolio Management**

Portfolio management becomes the focus on the Level 3 exam, so it really pays to learn the 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.

Variance

_{portfolio}= w

^{2}

_{1}*σ

^{2}

_{1}+w

^{2}

_{2}σ

^{2}

_{2}+ 2w

_{1}w

_{2}(correlation) σ

_{1}σ

_{2 }*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.

A little over a week left to the exam.

‘til next week, happy studyin’

Joseph Hogue, CFA