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Overview:

- Where should we invest?

- How much risk to take?

- How to reduce portfolio volatility?

Some of the inevitable questions that every trader goes through on a day to day basis, Quantitative Portfolio Management not only simplifies the solutions to these problems but also allows you to optimally allocate capital among different strategies.

QuantInsti brings you an exclusive interview with Prodipta Ghosh where he will share his insights and certain tricks of the trade.

Outline of the Interview

- Difference between buying a stock and creating a portfolio?

- How should one make investment decisions?

- How to optimize a portfolio for better returns?

- How to identify and minimize risk?

And so much more...

Speaker Profile:

Prodipta leads the Fin-tech products and platforms development at QuantInsti.

He is a seasoned quant & prior to joining QuantInsti, he spent more than a decade in the banking industry – in various roles across trading and structuring desks for Deutsche Bank in Mumbai & London, and as a corporate banker with Standard Chartered Bank. Before that, Prodipta worked as a scientist in India’s Defence R&D Organization (DRDO).

He is a graduate with a B.E. in Mechanical Engineering from Jadavpur University and has a postgraduate degree in management from IIM Lucknow.

Tuesday, 23rd July 2019

10:00 AM ET | 7:30 PM IST | 10:00 PM SGT

For the Webinar video, you can also visit: https://blog.quantinsti.com/quantitative-portfolio-webinar-23-july-2019/

Learn more about our EPAT® course here: https://www.quantinsti.com/epat/

OR Visit us at: https://www.quantinsti.com/

Like and Follow us on:

Facebook: https://www.facebook.com/quantinsti/

LinkedIn: https://www.linkedin.com/company/quantinsti

Twitter: https://twitter.com/QuantInsti

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- 1. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Quantitative Portfolio Management Strategies A Systematic Approach “Successful investing is anticipating the anticipations of others.” John Maynard Keynes (Economist)
- 2. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Why Portfolio Management What are we missing here? Uncertainties: `Best` stocks picked by anyone right now are just our best guesses given our current understanding (model) of the world. It is not perfect. Changing market: Best stocks, good strategies and winning signals are not static, they change over time, even if our current understanding was perfect! Context: Best stocks and good strategies are not unique. They are different for different investors even if our world model was perfect and we have a full 20/20 future vision! The technical terms are 1) risks 2) time dependence and 3) utility
- 3. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Which is the Best Strategy? Strategy-I: 18.4%, Strategy-II: 15.0%, Strategy-III: 19.1%, Strategy-II: 3.8%
- 4. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Returns from the Best Strategy Risk adjusted returns: 21.6% (scaled)
- 5. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. The Value from a Naive Portfolio Risk adjusted returns: 36.2% (scaled)
- 6. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. What is Portfolio Management Investment/ Strategy: A single expected source of returns streams Portfolio Management: A meta strategy to allocate capital based on risks and context, over a period of time. Strategy value: v= 𝟏 + 𝝓𝒕−𝟏 𝒔 𝒕 × 𝟏 + 𝝓𝒕 𝒔 𝒕+𝟏 … = (𝟏 + 𝝓𝒕−𝟏 𝒔𝒕)𝑻 𝟏 Portfolio value: 𝐩 = 𝟏 + 𝒘 𝒕−𝟏 𝒌 𝒓 𝒕 𝑵 𝟏 𝑻 𝟏 Building Portfolio: max 𝒍≤𝒘≤𝒖 𝔼𝑼 , 𝑼 = 𝒇(𝒑) Different types: How we define 𝑈 = 𝑓(𝑝) , (mean-variance optimization, Kelly optimization, risk-parity etc.) How we optimize it – static (per period and rebalance) vs dynamic (continuous rebalance), how we define constraints (long only, long-short, leveraged), and how we chose the set of returns streams (alpha strategies, factor portfolio, value portfolio etc.)
- 7. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. How to Build a Portfolio Building Portfolio: max 𝒍≤𝒘≤𝒖 𝔼𝑼 , 𝑼 = 𝒇(𝒑) Equally portfolio makes sense if #1: All the stocks (or assets or strategies) are exactly equivalent (a trivial case!) #2. If your 𝑈 function is product of the weights (for some reasons!) #3. You have a very high uncertainties around those returns stream. Remember regularization from data science? This is equivalent to a L2 regularization with a very high penalty. So high that maximization problem becomes effectively minimization of the penalty term. #4. Empirically, equal weighted portfolio does fairly good! But, if we have a good model (better than random), then we can do better!
- 8. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. How to Build a Portfolio We can do better if we can have good model of the world and define what we care about (utility function) more precisely in terms of our model variables Let’s be reasonable and assume #1. at least we can predict the expected returns and risks of our assets reliably and #2. We prefer higher returns for a given amount of risks, or a lower risks given a return This sets us up for the famous mean-variance optimization (MVO). It can also be shown this is (somewhat) equivalent to assume a quadratic utility.
- 9. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. How to Build a Portfolio A Simple Game of Luck: You pay $X dollars to play a betting game against the “house”. The game starts with $1 in the pot. At each turn the dealer toss a fair coin. If it is tails, you get whatever in the pot, else we move to the next turn with the house doubling the pot amount (i.e. $4, then $8 then $16 and so on). AKA St. Petersburg paradox. What is X. How much you will pay to play this game?
- 10. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. How to Build a Portfolio Risks: A measure of uncertainty. Ambiguity: Uncertainty in risks itself. In finance we typically use a “deviation risk measure” like standard deviation. Utility: a mathematical formulation of how we feel about our wealth – how much an extra dollar is worth to you, given your current dollar wealth. Risks vs Utility: They are related through “risk premium”, how much lower certain returns one is ready to accept to avoid uncertainty (certainty equivalence). Risk premium exists because we assume most of us are risk averse (given same returns, prefer a lower risk. If most investors in an economy are indifferent between a 3% p.a. certain returns (like a bank deposit or treasury bill), compared to an expected 8% p.a. returns from the broad equity market, the risk premia is 5%.
- 11. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. How to Build a Portfolio This leads us to 𝔼𝑼 as a of mean of W (𝝁) and variance of W(𝝈 𝟐 )! The central optimization problem becomes a mean-variance optimization (MVO) problem! AKA Modern Portfolio Theory or MPT. Risk Aversion: 𝔼𝑼 𝑾 + 𝝐 < 𝑼 𝑾 Risk Premium: 𝝅 | 𝔼𝑼 𝑾 + 𝝐 = 𝑼 𝑾 − 𝝅 , depends on 𝝐, shape of 𝑼 and current wealth! But for small risks, a function of variance of 𝝐 A special case: 𝐔 𝑾 = 𝑾 − 𝝀 𝟐 𝑾 𝟐 , 𝝀 > 𝟎 Alternatively, if you do not like quadratic utility, we can just assume all asset returns are normal, then wealth distribution is also normal. So finding max of 𝔼𝑼 again becomes a mean-variance game, i.e. MPT!
- 12. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. MPT, CAPM and Factors Modern Portfolio Theory: We prefer lower risks for a given amount of returns. We also can compute expected returns and risks with good confidence. Let’s randomly allocate a range of weights for each of our assets, and chose the best portfolio. Let’s see how it works using Excel! Optimization: min 𝒍≤𝒘≤𝒖 𝝈 𝟐 | 𝝁 = 𝝁∗ , 𝝁 = 𝒘 𝑻 𝑹 & 𝝈 = 𝒘 𝑻 𝚺𝒘, 𝒐𝒓 m𝑎𝑥 𝒍≤𝒘≤𝒖 𝔼𝝁 − 𝟏 𝟐 𝝀𝝈 𝟐 MPT: Tells us given market prices, what an intelligent investors will do (allocate between a market portfolio and risk free asset) What if we Flip it? Given intelligent investors and market equilibrium, what that means for market prices – this leads to the door to an asset pricing model, namely Capital Asset Pricing Model or CAPM.
- 13. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. MPT, CAPM and Factors 𝔼𝑅 = 𝑅𝑓 + 𝛽𝑖 𝔼𝑅 𝑀 − 𝑅𝑓 CAPM: gives us the basic mathematical foundation for value investing! It models the required rate of return or fair value. If we have a good model that tells us the expected return is higher (lower) we can buy (sell) the asset. According to CAPM. No excess returns for diversifiable risks. But ONLY idiosyncratic risks are rewarded! The inspiration for stock picking. Typical value investors will assess a few investments, bet on their idiosyncratic upside, and hedge the market (systematic) risk. Notice how MPT fundamentally changes our concept of risks. Not standard deviation, but covariance to market portfolio is what matters! 𝛽 is the risk, not 𝜎! 𝑅 = 𝛼 + 𝛽𝑖 𝑅 𝑀 − 𝑅𝑓 + 𝜀
- 14. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. MPT, CAPM and Factors 𝑅𝑖,𝑡 = 𝑎𝑖 + 𝛽𝑖,𝑗∆𝐹𝑗,𝑡 + 𝜖𝑖,𝑡 𝑗 APT: A framework of (unspecified) factors that explains asset returns. Unlike CAPM it provides no economic explanation of what these factors can be. Are the idiosyncratic risks really so? Welcome to factor investing, pioneered in the 70s, popular after 2008 crisis! Fama French: Precisely 3 factors. They are called size (large cap vs. small cap), value (book-to-market rich vs. cheap) in addition to the market factor 𝔼(𝑅𝑖,) = 𝑅𝑓 + 𝛽𝑖,𝑗 𝑅𝑃𝑗 𝑗 What is beta, alpha? Beta – coefficient in the above equation with only market factor. Alphas are tricky – what if 𝛽 and ∆𝐹 time-invariant and positive? – pure alpha! What if 𝑅𝑃 is stable but 𝛽 varies? – factor allocation! What if 𝛽 stable but 𝑅𝑃 varies? – factor timing! What if everything is unpredictable? – focus on α, stock picking!
- 15. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. The Issues with Value In CAPM world, the job of investors is to find assets with high expected residual returns (don’t get paid for systematic risks). The issue with value investing – focus on concentration and idiosyncratic risks. Factor Models say most of this residuals can be explained by other factors – known as risk factors. In such a world, the job of the investors is to find factors with high risk adjusted expected returns and design portfolios to capture this. We systematically probe the drivers of the markets – than doing in-depth research on a few companies. Although this sounds just a continuation, this approach is fundamentally different! We move from discretionary value research to quantitative factor research (usually called alpha streams)
- 16. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Discretionary vs. Quant Asset manager A is a discretionary manager and follows 10 stocks diligently. Asset manager B is a systematic manager and have enough computational power to track 500 stocks. Investors seek outperformance and confidence. Question #1: What is the hit ratio for A to achieve outperformance in at least 50% (total 5 stocks) of his portfolio with at least 95% probability. What is for B? -15% 5% 25% 45% 65% 85% 105% 10% 20% 30% 40% 50% 60% 70% 80% 90% Probabilityofsuccess Investing Skills A B Pr 𝑛 𝑁, 𝑝) = 𝐶𝑁 𝑛. 𝑝 𝑛 . (1 − 𝑝) 𝑁−𝑛 𝑃 = 1 − Pr 𝑖 𝑁, 𝑝) 𝑛 𝑖=1
- 17. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Value vs. Quant Discretionary Systematic/ Quant Small N (usually) Large N (usually) Edge is deep, proprietary insights Edge is superior info processing Ideally offers superior upside Ideally offers superior consistency It is NOT one OR the other, it is one AND the other The fundamental law of investment management: 𝐼𝑅 ≈ 𝐼𝐶 . 𝑁. 𝑇𝐶
- 18. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Optimizing Factor Portfolio It is very similar than before. We first decompose our returns to factors, then express the variance in terms of factors covariance + asset covariance, and optimize using a chosen utility function – like say mean-variance. Note, here we have two parameters (unlike just one, 𝜆 before! One each for the covariances). m𝑎𝑥 𝒍≤𝒘≤𝒖 𝑹 𝑻 𝒘 − 𝒘 𝑻 𝝀 𝑭 𝑿 𝑻 𝑭𝑿 + 𝝀 𝑨 𝑫 𝒘 𝒓 = 𝑿𝒇 + 𝒖, 𝒄𝒐𝒗 𝒓 = 𝑿 𝑻 𝑭𝑿 + 𝑫 Theoretically asset covariance 𝑫 is diagonal, under the assumptions that 𝒇 and 𝒖 are independent, and so are the individual components of 𝒖. These 𝝀 are also known as price of risk.
- 19. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Other Optimization Techniques The other popular methods are Kelly and Risk Parity For Kelly, our 𝑼 is different, it is 𝒍𝒏 𝟏 + 𝒓 𝒇 + 𝒖 𝒌 𝒓 𝒌 − 𝒓 𝒇 𝒏 𝒌=𝟏 This is just optimizing wealth accumulation, than mean vs. variance. In fact both MVO and Kelly follows from a general class of 𝑼 known as constant relative risk aversion (CRRA). All methods following this will be independent of starting wealth!! Mathematically great, but what about practicality? Interesting points about Kelly: Theoretically dominate all others in minimum time to reach a target wealth level! In the long run, it almost surely dominates But this comes at a cost of riskier short terms! Optimization with most aggressive risk aversion parameter. Also very sensitive to estimation errors in returns. And high volatility (especially when going is good, may be not too bad!). Most usually follow a factional- Kelly approach to avoid risk of ruins!
- 20. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Other Optimization Techniques This is mostly empirical, (while it is possibly to construe an utility function here, hard to make any economic sense!) Individual risk contribution: 𝜎𝑖 = 𝑤𝑖 𝜕𝜎 𝜕𝑤 𝑖 is equal!, Note 𝜎 = 𝜎𝑖 where 𝜎 = 𝑤 𝑇 𝜎𝑤 We do not talk about expected returns, only risks, which are usually more stable and easier to estimate with better confidence. Less sensitivity to model errors!
- 21. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. When to Use What If we are quite sure about our models, mean-variance or Kelly offers a great choice. Kelly is best in the long run, but risky in the short term (volatility pumping). So perhaps a good choice if you are young or can afford risk of ruins! If we don’t trust any models, as we have seen, equal-weighted portfolio is a choice On the models – expectation based on CAPM only can be back-ward looking, so we try to improve with a factor model. Or even a better model if you can imagine and test one. All these optimization problems are very similar, the right constraints can be on sign of weights (long-only portfolio), on industry/ sector/ asset class/ factors exposure etc. If our returns models are NOT good, but risks models are okay, we can go for risk parity (usually risks are more stable than returns). This is defensive with decent empirical performance
- 22. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Portfolio Under Uncertainty We can use any methods but we may run in to difficulties. For example, alpha strategies (say a few intraday trading strategies) are by definition uncorrelated. So an MVO on them will lead us to whole weight given to the best strategy in the retrospect. What if we are wrong going forward? Other, more recent, methods of managing portfolio of assets are strategies may help. Examples are Ensemble strategies (we already seen the average portfolio), with (potentially dynamic) voting weights Regime-switching portfolio – where we dynamically detect change in model parameters and switch models (say using a change point analysis) No-regret Strategy – Adaptive weighing of strategies based on recent performance – usually based on returns (with possibilities of risk adjusted measures, e.g. Sharpe)
- 23. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Portfolio Under Uncertainty If slot machines were your strategies, how would you play them? Strike a balance between exploration vs. exploitation (through a learning rate) and change weights dynamically – a case of online reinforcement learning 𝑤𝑖 𝑡+1 = 𝑤𝑖 𝑡 exp( 𝜂𝑥𝑖 𝑡 𝑾 𝑡. 𝒙 𝑡) 𝑤𝑗 𝑡 exp( 𝜂𝑥𝑗 𝑡 𝑾 𝑡. 𝑿 𝑡)𝑁 𝑗=1 Kind of follow the leaders – will not work in a sideways markets. Multiplicative updates can lead to concentration (can be controlled by learning rate)
- 24. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Open House Q&A
- 25. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. Webinar Video Link https://youtu.be/u5UUjHZQCFk
- 26. www.quantinsti.com CONFIDENTIAL. NOT TO BE SHARED OUTSIDE WITHOUT WRITTEN CONSENT. THANK YOU! For further queries reach out to: corporate.team@quantinsti.com For queries on Quantra Blueshift: blueshift-support@quantinsti.com

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