What you want to know about Real Estate Valuation, Time Series Modeling, Pensions, Parity Relations, and Treynor Black...

<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>> Ok, this is part of the CFA curriculum that typically doesn’t get studied a lot because people think they know it implicitly. Well, I was in the mortgage business for five years, and get tripped up here time and time again. ____________________________________________ First, you need to calculate a capitalization rate. There are three testable ways to do this. 1. Market Extraction Method. Easy, just NOI/MV 2. Band of Investment Method. This only works with comparables that are mortgaged at the same loan to value (have the same debt/equity mix). You add a sinking fund factor to the cost of the mortgage, which is: i / 1+(i^n)-1 where i = interest rate on mortgage and n = number of years in mortgage Add the sinking fund factor to mortgage cost, and calculate WACC to find the cap rate. 3. Built-Up Method. Don’t just think you can add risk premia. You need to know WHAT risk premia to add. Take the pure rate (Risk free rate like in CAPM) + liquidity premium + recapture premium + risk premium __________________________ Now, with that said, you can calculate your Cap Rate. But, how do you calculate the value of the property? There are two ways. 1. First, derive the Gross Income Multiplier = Sales Price of comparables / Gross annual income of comparables Second, take the gross income of your subject property / Gross Income Multiplier to get Market Value. ***This will yield an upwardly biased price because it only incorporates gross income not costs, whereas the Direct Capitalization Approach uses Net Operating Income. 2. Direct Capitalization Approach = the same as the above but with Net Operating Income instead of Gross. __________________________________ Next, you can analyze cashflow returns by using the IRR method. This is helpful is you have to surpass a hurdle rate required by a group of investors. 1. IRR Method. Treat each annual Cashflow After Tax as CF1, CF2, CF3…CFn on your BA II Plus calculator. Treat the After tax Equity Reversion as the Terminal Nonoperating Cashflow (remember to add the CFt to that number when putting the data in your calculator!). Input the cap rate as your I/Y, or a “hurdle rate” and solve for IRR. <<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>> Ok, so I’ve seen a lot of grief about the time series stuff that can pop up on exams. I also experienced myself recently in the morning exam from Schweser in Volume I (#3) on that time series shiznit. When I went back over the answers, I couldn’t believe I actually got so" “flummoxed” that I missed the question about testing the residuals… ___________________________ First, understand what investment you’re working with. Are you working with data that is best predicted by other data represented as independent variables? This is cross sectional data. Or, are you working with data that is best predicted by its own past values? This is time series. If we use a time series data, plot the data and check for covariance stationarity (a good thing). What is this? Basically, it means that the data sticks around its mean, and there is a finite variance. If the data just skyrockets off the chart, it exhibits a trend and is not covariance stationary. If it exhibits a trend, is it a linear trend? Or, a loglinear trend? A linear trend is data that increases at a constant number. A loglinear trend is data that increases exponentially, or at a constant % rate. Also, note for seasonality and a regime change when plotting the data. What’s that? Sales data will be seasonal, with spikes in the 4th quarter. Interest rate data will experience a regime change, as the US Fed pursues different policies under different Fed Chairmen (think Alan Greenspan versus Paul Volcker). If the data is not covariance stationary, first difference it! This is EASY. If you’re working with monthly sales data, and you’re forecasting May’s sales data, take the difference between April and March, March and February, February and January, and so on. Remember, first differenced data will have n-1 observations. If the model you are using is an AR model, it may likely exhibit a random walk. What is this? This essentially means that the current period value is the prior period value multiplied by a random value (b1). Think of currency movement here guys. A random walk is NOT COVARIANCE STATIONARY, and has no mean reverting level (b0 / 1-b1). First difference this data to make it covariance stationary. Do the same for random walk with drift data (on this, b0 = 1, not 0 as in random walk without drift). ------------------------------ As a quick aside, one set of time series data can be used to explain another set of time series data. In this event, a unit root can occur (think of this as “divide by 1”). If you are told that one set of data has a unit root, but the other does not, you can’t proceed. But, if both have a unit root, and the Engle-Granger Dickey-Fuller t-test statistic determines that both sets of time series data are COINTEGRATED, then go ahead and proceed with the model. ------------------------------ Back to the AR model. Continue to plot the data, confirm covariance stationarity (aka stationary). Now use the Durbin Watson statistic to test for serial correlation. This can come in positive and negative forms. On this, you test the autocorrelation of the residuals. The standard error for this is (1 / square root of #observations). What is the autocorrelation of the residuals? Just another fancy way of taking each observation’s residual [(actual Y - expected Y)^2] and testing them for autocorrelation (aka serial correlation) with the DW statistic. Assuming no statistical significance, serial correlation is not a problem. Let’s say serial correlation is a problem. Well, we use an AR model in that case. Serial correlation does not misspecify an AR model, because the independent variables are lags of the dependent variable…of course the data is correlated with itself! DUH! Remember that an AR(1) with a seasonal lag sometimes can look like an AR(2), but it’s not! Don’t get tripped up on that. BUUUT, if serial correlation is a problem, just insert another independent variable (lag of the dependent) and you get an AR(2). If serial correlation is still a problem, repeat and you get an AR(3). Do so until no problem. Now, test for ARCH. Take the original residuals and square them. Regress each residual upon its prior period residual, and so on. If b1 is statistically significant from zero, you’ve got an ARCH process folks. Use generalized least squares method to correct for ARCH. This provides a better “fit” for the line. FINALLY, perform an out of sample forecast performance evaluation and compare it to the RMSE. What is the RMSE? This is the in sample forecast performance evaluation (your theory versus the real world) and is simply the square root of the average of the standard errors. Just take all the standard errors (aka residuals, aka “e”), square them, and get their arithmetic average. Now, take the square root. That’s your RMSE. You want a LOW RMSE…think of it like your Accruals ratios in FSA. You want the lowest number possible. Why? You’re dealing with ERRORS friend! That’s that… <<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>> Ok, so I’m going to assume that you already know to Schweser formulae for pensions. The problem is that there are quite a few testable areas simply not covered, or at least, well known. This is an attempt, even if frail, to assist in those matters. _______________________________________ 1. Did you know the difference between Actual and Expected ROA is reported in OCI, Equity? 2. GAAP reports prior period service costs in OCI and amortizes them over the remaining (employee) service life. IFRS expenses fully vested benefits and amortizes unvested benefits according to the corridor approach. 3. The corridor approach is simple. Basically, if your unamortized items are greater than 10% of either the OPENING values of PBO or Fair Value Plan Assets, then you can either amortize the full amount or only that above 10% (who would seriously amortize the full amount?)… 4. Actuarial g&l stem from 2 factors: assumptions used in determining the PBO and difference between actual and expected ROA. Long term, this should approach zero. Short term, it’s due to market fluctuation. ECONOMIC PENSION EXPENSE (and adjustments) 1. This is what you should do as an analyst. The economic pension expense (think economic income vs accounting income) can be calculated in two ways. One, subtract the change in Funded Status from Contributions. Two, take the change in the PBO, addback Benefits Paid, and subtract Actual ROA. 2. CF Statement adjustments. If economic pension expense is GREATER than funded status (which is Fair Value of Plan Assets - PBO), then treat this as BORROWING. Reduce CFO and increase CFF by the after tax amount. If vice versa, treat this as PRINCIPAL PAYDOWNS and increase CFO and reduce CFF by the after tax amount. 3. Income Statement adjustments. Back out all pension expense components. (Remember, GAAP presents this as a net amount, and IFRS can either do that or itemize) Addback interest costs to interest expense. Addback current service costs to SG&A. Addback ACTUAL ROA to nonoperating income (note this is not expected ROA here folks as it is in pension expense). Disregard the amortized items. 4. Balance Sheet adjustments. Change the pension asset/liability reported to reflect Funded Status. Say you have a $500 reported pension ASSET, but its funded status is $300. Change it to $300. Let’s say the tax rate is 40%. The difference of $200 will be split into Tax Deferred Liabilities of $80 and OCI (Equity) of $120. Balance sheet should balance. A LITTLE NOTE ABOUT PENSION ASSET ON BALANCE SHEET REPORTING HERE IFRS and GAAP are different. We all know that GAAP simply reports the funded status on the balance sheet. But, did you know that the unrecognized transition liabilities, prior service costs, and actuarial losses are all added up (yes, treated as assets, odd, I know) and placed in OCI (Equity)? Also, we all know the IFRS equation to report pension asset on the BS. But, did you know that IFRS requires you to report the LOWER of that figure or the sum of: PV future refunds + unrecognized actuarial loss + unrecognized prior service costs? The difference is disclosed in the footnotes, and if the latter option is chosen, will be the transition liability. <<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>> This confused me for some time until I created a simple notecard, and it goes a little something like this… Interest Rate Parity – The forward premium/discount simply is the interest rate differential. The country with the lower risk free rate will experience a currency appreciation and vice versa. Purchasing Power Parity – The expected spot rate (NOT FORWARD) simply is the inflation differential. The country with the lower inflation will experience currency appreciation and vice versa. (this is relative PPP) International Fischer Relation – IRP and (relative) PPP combined. The inflation differential equals the interest rate differential. What really important thing does this imply? REAL RATES ARE CONSTANT. *Remember: nominal rates equal real plus inflation. Uncovered Interest Rate Parity – PPP and Fischer are combined to state that the expected spot price is explained by the interest rate differential (don’t confuse this with interest rate parity alone). This is “uncovered” because it’s unhedged, there is no forward contract here. Covered uses a forward contract to hedge the ‘bet’. Foreign exchange expectation relation – forward premium/discount equals expected exchange rate movement, or expected currency appreciation/depreciation. ________________________________________ Notes: *Covered Interest Arbitrage simply is like uncovered IRP, but uses a forward contract. Simply borrow DC at RF and exchange to FC. Lend the FC at its own RF, and use a forward to repatriate the currency at expiry. 1. Flow market approach - high economic activity and low unemployment lead to depreciated currency, and higher rates b/c of increased inflation. 2. Asset market approach - high economic activity and low unemployment leads to increased foreign direct investment b/c of high rates used to fight inflation, which leads to currency appreciation. 3. Real Exchange Rate = Nominal x (Price Levels foreign currency/ Price Levels domestic currency) <<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>> SUMMATION The Treynor Black model combines market inefficiency and modern portfolio theory. In other words, it combines Active and Passive (indexing) management. This derives from two arguments in favor of active management: Economic (active managers promote market efficiency by arbitraging away mispricings and restoring equilibirum pricing) and Empirical (studies show active management just plain works). ______________________________________ STEPS Step 1 - Develop expectations for passive portfolio M (think “Market” portfolio like in Markowitz’s efficient frontier) Step 2 - Identify mispriced assets Determine each asset’s alpha ------> Alpha = Return on Asset i - Expected Return as calculated by CAPM Step 3 - Determine the optimal weighting in Active Portfolio “A”. We weight the alphas, Betas, and residual variance (think quant = ERROR TERM here folks). Step 4 - Comibine Active “A” and Market “M” portfolios to form Portfolio “P” by summing the squared Sharpe Ratio of M and Information Ratio of A. Choose the combination with the highest overall squared ratio. (Think R2 in quant, Sum of Squares) Step 5 - Allocated to the optimal Portfolio “P” the risk free rate depending upon investor’s desired risk levels within the Capital Allocation Line (CAL). YOU NEED TO KNOW how to determine the investor’s position in the optimal risky portfolio P and the risk free rate (Step 5). This is denoted as -------> -----> y = E(R market portfolio M) - Rf / 0.01 x A (investor’s risk coefficient) x Variance of Portfolio M _____________________________________________- The CFA text says you don’t need to know the calculations for Treynor Black. However, that above equation of solving for the investor’s weighting in “y” (optimal risky portfolio “P”) is not included. Check the text if you disbelieve me. Also, remember to adjust analyst’s alphas by multiplying them by R2.

Amazing! Thanks!

Can someone spot check this please? (cpk?) Seems dangerous if a tad off.

Economic pension expense calculated using these two ways yields different answers for the mock exam question. Right?

Hey David, thanks, great series. One note tho: you can’t use DW for time-series where y is regressed on lagged values of itself.