Monday, May 12, 2014

benchmark a static factor model against CAPM

http://bigblog.tanbin.com/2014/04/risk-premium-clarified.html explains ...

Let me put my conclusion up front -- now I feel these factor models are an economist's answer to the big mystery "why some securities have consistently higher excess return than other securities." I assume this pattern is clear when we look long term like decades. I feel in this context the key assumption is iid, so we are talking about steady-state -- All the betas are assumed time-invariant at least during a 5Y observation window.

There are many steady-state factor models including the Fama/French model.

Q: why do we say one model is better than another (which is often the CAPM, the base model)?

1) I think a simple benchmark is the month-to-month variation. A good factor model would "explain" most of the month-to-month variations. We first pick a relatively long period like 5 years. We basically "confine" ourselves into some 5Y historical window like 1990 to 1995. (Over another 5Y window, the betas are likely different.)

We then pick some security to *explain*. It could be a portfolio or some index of an asset class.

We use historical data to calibrate the 4 beta (assuming 4 factors). These beta numbers are assumed steady-state during the 5Y. The time-varying (volatile) factor values combined with time-invariant constant betas would give a model estimate of the month-to-month returns. Does the estimate match the actual returns? If good match, then we say the model "explains" most of the month-to-month variation. This model would be very useful for hedging and risk management.


2) A second benchmark is less intuitive. Here, we check how accurate the 2 models are at "explaining" _steady_state_ average return.

Mark Hendricks' Econs HW2 used GDP, recession and corp profits as 3 factors (without the market factor) to explain some portfolios' returns. We basically use the 5Y average data (not month-to-month) combined with the steady-state betas to come up with an 5Y average return on a portfolio (a single number), and compare this number to the portfolio actual return. If the average return matches well, then we say ..."good pricing capability"!

I feel this is an economist's tool, not a fund manager's tool. Each target portfolio is probably a broad asset class. The beta_GDP is different for each asset class.

Suppose GDP+recession+corpProfit prove to be a good "pricing model", then we could use various economic data to forecast GDP etc, knowing that a confident forecast of this GDP "factor" would give us a confident forecast of the return in that asset class. This would help macro funds like GMO making asset allocation decisions.

In practice, to benchmark this "pricing quality", we need a sample size. Typically we compare the 2 models' pricing errors across various asset classes and over various periods.

When people say that in a given model (like UIP) a certain risk (like uncertainty in FX rate movement) is not priced, it means this factor model doesn't include this factor. I guess you can say beta for this factor is hardcoded to 0.

No comments:

Total Pageviews

my favorite topics (labels)

_fuxi (302) _misLabel (13) _orig? (3) _rm (2) _vague (2) clarified (58) cpp (39) cpp_const (22) cpp_real (76) cpp/java/c# (101) cppBig4 (54) cppSmartPtr (35) cppSTL (33) cppSTL_itr (27) cppSTL_real (26) cppTemplate (28) creditMkt (14) db (65) db_sybase (43) deepUnder (31) dotnet (20) ECN (27) econ/bank` (36) fin/sys_misc (43) finGreek (34) finReal (45) finRisk (30) finTechDesign (46) finTechMisc (32) finVol (66) FixedIncom (28) fMath (7) fMathOption (33) fMathStoch (67) forex (39) gr8IV_Q (46) GTD_skill (15) GUI_event (30) inMemDB (42) intuit_math (41) intuitFinance (57) javaMisc (68) javaServerSide (13) lambda/delegate (22) marketData (28) math (10) mathStat (55) memIssue (8) memMgmt (66) metaProgram` (6) OO_Design (84) original_content (749) polymorphic/vptr (40) productive (21) ptr/ref (48) py (28) reflect (8) script`/unix (82) socket/stream (39) subquery/join (30) subvert (13) swing/wpf (9) sysProgram` (16) thread (164) thread_CAS (15) thread_cpp (28) Thread* (22) timeSaver (80) transactional (23) tune (24) tuneDB (40) tuneLatency (30) z_ajax (9) z_algoDataStruct (41) z_arch (26) z_arch_job (27) z_automateTest (17) z_autoTrad` (19) z_bestPractice (39) z_bold (83) z_bondMath (35) z_book (18) z_boost (19) z_byRef^Val (32) z_c#GUI (43) z_c#misc (80) z_cast/convert (28) z_container (67) z_cStr/arr (39) z_Favorite* (8) z_FIX (15) z_forex (48) z_fwd_Deal (18) z_gz=job (33) z_gzBig20 (13) z_gzMgr (13) z_gzPain (20) z_gzThreat (19) z_hib (19) z_IDE (52) z_ikm (5) z_IR_misc (36) z_IRS (26) z_javaWeb (28) z_jdbc (10) z_jobFinTech (46) z_jobHunt (20) z_jobRealXp (10) z_jobStrength (15) z_jobUS^asia (27) z_letter (42) z_linq (10) z_memberHid` (11) z_MOM (54) z_nestedClass (5) z_oq (24) z_PCP (12) z_pearl (1) z_php (20) z_prodSupport (7) z_py (31) z_quant (14) z_regex (8) z_rv (38) z_skillist (48) z_slic`Problem (6) z_SOA (14) z_spring (25) z_src_code (8) z_swingMisc (50) z_swingTable (26) z_unpublish (2) z_VBA/Excel (8) z_windoz (17) z_wpfCommand (9)

About Me

New York (Time Square), NY, United States
http://www.linkedin.com/in/tanbin