Portfolio Management 101
By pjain Published Aug. 2, 2020, 8:19 p.m. in blog Invest
 Portfolio Management Theory
 Endowments and Portfolio Asset Allocation
 Diversification near free lunch
 Return and Standard Deviation
 Only way to get more return is another point on EF with adding more risk
 Math of Portfolio Management
 Alpha and Beta
 Consider 2 asset portfolio  popular 60/40 stocks/bonds
 RISK PARITY Portfolios  optimal Sharpe Ratio even with Leverage boosts
 Sharpe Ratio
 Kelly's Ratio for betting
 LONG TERM PORTs  Need to grow the money  power of compounding
 Everyone is doing EF, Trying to Find Alpha  REALLY hard to do!
 EARN my FEES by taking more risk!
 HERDS: Synchronous Action in Markets can Crash  Connected
 Risk Assessment
 Reference
 Mathematics Applications in Modern Finance
 Financial scientific and Data driven Planning
 Mathematics Applications in Modern Finance
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 riskreturn
 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 strongenough 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 812% as cash to ride out.
Consider special case of 2 assets
Rp = w1R1 + (1w1)R2 R1=R2,s1=0, s2 not 0, corr=0
Math of Portfolio Management
Rport = Sumin( 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 pumpanddump 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.
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 datadriven insights from MIT professors. Prereq: Basic Probability and Statistics, Calculus
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