Portfolio Management Theory

Endowments and Portfolio Asset Allocation

• Alternative intensive, low equity
• Long Term horizons - 10+ years
• More technology, data driven, analytics

• Need to be reasonably liquid as support AND cant support major drawdown ~40% of university budget year after year funding

• Yale Model - use external funds, alternative intensive, low equity

• Harvard Model - manage LOT more internally - hard to find
• Small Univ ?, Did very good with lazy low cost ETFs

Diversification near free lunch

Sharpe Ratio * I had lots of traders reporting to me - all saying great strategy guaranteed returns - give me higher llimit - Boils down to RISK MANAGEMENT - ALLOCATING limits in trading is key to that - Let them prove themselves

Return and Standard Deviation

• Return can be modelled for stochastic events by an expected value of probability*return

• Markowitz, Sharpe - Efficient Frontier, Modern Portfolio theory got Nobel Prize

Consider cases for risk-return

• Cash CDs, Money Markets, etc. has low fixed return and nearly 0 variance (FDIC safe? but Cyprus/Indian PSB accounts at risk)
• Coin flip - 0 expected value, equal extremes bifurcated so std.deviation = 1
• Lottery - virtually guaranteed to lose all money so return = -100%, Variance is very small 0.000..1% get something so near certainty std dev=0
• VC expect 1/10 to IPO hit out of ballpark, 3+ to be/acq so 2x invest as loan, rest lose all - so high returns ~15%, high variance
• ETFs have lower variance than single stocks but lower returns
• Bonds usually low volatility, lower returns (returns really low since QE/Financial repression of 2008+) but allowing negative rates Race to NIRP
• Commodities have more volatility than stocks, but returns may not really be more - same for Forex - too much skill required.
• PE/HF funds can deliver alpha with strong-enough returns and actually far less risk than VC but strict domain/strategy expertise = backtest/verify

Why is it an Efficient Frontier EF of BLENDED ASSETS?

• Consider the scatter plot of returns and variability.
• You could create a regression curve, but EF is more - you can blend a few assets to optimize the minimum risk a given maximum return

• Only way to get more return is another point on EF with adding more risk

CAP Capital Allocation - with Cash

• If you add some riskless asset like cash (or near cash) to portfolio, this is a tangent to the EF based on how much risk you want
• The cash percentage of allocation also provides the liquidity, eg if you want to ensure 4% of portfolio cashout every year, but max drowdown, you may need to keep say a multiple of 4% * N years or poor returns as cash to avoid selling at worst times - eg if a bear market lasts <2 years, you may keep 8-12% as cash to ride out.

Consider special case of 2 assets

Rp = w1R1 + (1-w1)R2

R1=R2,s1=0, s2 not 0, corr=0

Math of Portfolio Management

Rport = Sumi-n( wi* Ri)        - linearly allocate each asset 
variance sigma_p^2 = wavgvector x CovarianceMatrix

Alpha and Beta

Rp - Rf = alpha + beta*(Rm - Rf) + E

- Rp = portfolio return
- Rf = riskfree return - cash or govt bonds
- Rm = Benchmark return eg SPY or BND
- E - ??

Consider 2 asset portfolio - popular 60/40 stocks/bonds

• Before 2000 60/40 was hugely popular
• stock volatility is higher, and returns higher
• bonds provide ballast

2008 GFC

• Bond and Gold markets rallied massively

RISK PARITY Portfolios - optimal Sharpe Ratio even with Leverage boosts

• Edward Chan term - ALLOCATE RISK ie RISK PARITY not asset allocation - adding some leverage
• DIVERSIFICATION Higher return, lower risk - free lunch - Markowitz
• Needs REBALANCING to achieve this magic - can get lower risk, by doing this!
• LEVERAGE to boost returns

Sharpe Ratio

Sharpe Ratio = (Rp - Rf) / sigmaPort

• This is risk adjusted excess return

Kelly's Ratio for betting

• How much to bet up based on your winning probability p

  f = 2p - 1

  • 1 if 100% confidence - bet it all and more!
  • -1 put 100% on OTHER side if 0 sure of losing (fixed match by coopting player) - bet on other side
  • 0 DON'T BET - if don't know 50/50 coin flip - sadly this is what most people do
  • if lottery then p=-1 - basically f= -3 NEVER bet
  • Slots if pay 45:55 i.e. p= 0.45 - don't bet in long term or make very small bets i.e. 10% of your cash pile - don't GO ALL IN!

LONG TERM PORTs - Need to grow the money - power of compounding

Everyone is doing EF, Trying to Find Alpha - REALLY hard to do!

• If everyone is doing 60/40 or Risk Parity portfolios, they will not be able

EARN my FEES by taking more risk!

HERDS: Synchronous Action in Markets can Crash - Connected

• Millenium Bridge in London - supposed to resist crashing, but do this by swaying horizontally. But as people walk in sync, the resonance and tend to INCREASE sync and walk lockstep to keep steady as bridge sways. This is a form of herd instinct.

• This happens if you take a set pf metronomes on solid horizontal surface that doesn't move (unconnected) they will be random and not sync up. Bug if you put them on a horizontal surface that sways eg by putting on a board on top of two soda cans, now the action of swinging metronome, faces reaction. The metronomes are now connected in complex manner. Without a "human brain" or any programming, over time, the best way they can minimize the energy reaction is to sync to the motion, eg all metronomes will sync up pretty fast.

• Now in markets made of humans, there are a number of actions which cause this sync up!

  • FOMO on upside - people piling in at the top as huge returns come
  • MEDIA lags not leads - talking heads pump-and-dump or apologize for low performance!
  • FEAR FACTOR on way down!
  • Lots more to fall - IT AINT OVER TILL FAT LADY SINGS - DONT CATCH A FALLING KNIFE
  • TURNAROUNDS REALLY HARD - like a raging train/bear - hard to slow,stop,and start to build speed in other direction

Risk Assessment

Reference

Courses

• MIT 18.S096 Topics in Mathematics with Applications in Finance, Jake Xia, Fall 2013 This lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations.
  • MIT Open Portfolio Management

Mathematics Applications in Modern Finance

Pricing data

• Historical regression, patterns, TS - but don't understand it

Statistical Modeling

Behavior Data and Analytics

Fundamental modeling - try to understand what is behind data patterns

Reference

Courses

Financial scientific and Data driven Planning

How to understand something?

• Data Driven - gather, clean challenge
• Models for the domain, Simple models - why
• Lessons from Others
• Advice from mentors, Gurus, Experts - are they unbiased
• Personal reflection - know oneself
• Put it together - WRITTEN plan - how
• Execution, discipline, Timing - when
• Retrospective - what is working, what is not - very much a data driven personal review

Mathematics Applications in Modern Finance

Reference

Courses

• MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013 Instructors: Peter Kempthorne, Choongbum Lee, Vasily Strela, Jake Xia Key terms and concepts related to financial products, markets, and quantitative analysis. Course Page

• MITx 15.415.1x Foundations of Modern Finance I A mathematically rigorous framework to understand financial markets delivered with data-driven insights from MIT professors. Prereq: Basic Probability and Statistics, Calculus