Main summary financial modelling
Week 1. Introduction
What is a quantitative model?
Financial modeling refers to asset pricing, return prediction, portfolio optimization, risk
measurement.
Model classifications (i):
1.Empirical (data driven) vs. theoretical model
- Empirical model tries to describe underlying data generating process as good as possible: from data
to model
- Theoretical model makes testable predictions based on abstract reasoning and set of assumptions:
from theory to model.
2. Deterministic vs. probabilistic (stochastic) model
- Deterministic model does not have random/uncertain term -> e.g. CAPM
- Probabilistic model does have random/uncertain term -> e.g. regression
3. Discrete vs. continuous variables model
- Discrete variable can take only discrete (specific) values -> binominal tree
- Continuous variable can take any value within certain range -> BS model
4.Discrete vs. continuous time model
- Discrete time: value of variable can change at fixed points in time (binominal tree)
- Continuous time: value of variable can change at any point in time (BS model)
5.Cross-sectional vs. time-series vs. panel data model
- Cross-sectional: comparing multiple units (companies, stocks) at point in time
- Time-series: track one unit (company, stock, country) over time
- Panel: Track multiple units over multiple time periods.
Model optimization
Models often involve some type of optimization (max/min output var)
Two main approaches:
1. Analytical: use calculus to derive first-order condition and set to zero.
2. Numerical: use brute force approach (try many different value of input variables)
Model Simulation
Monte Carlo simulation is powerful computer-based technique used to analyze and account for
uncertainty in financial decision making.
Model Risk
“Potential loss institution may incur as consequence of decisions that are principally based on the
output of internal models, as a result of errors in the development, implementation, or use of such
models”.
Sources of model risk:
- Specification (design)
- Implementation: spreadsheet/programming flaws, wrong input, wrong cell reference.
- Application (scope) function creep (used for purposes it was not designed for),
misinterpretation of model outputs
, - Environment: time-varying parameters, relations break down (regime shifts)
Module 1.1: Introduction to hedge funds
What are hedge funds: A private investment pool, open to institutional or wealthy investors, that is
largely exempt from SEC regulation and can pursue more speculative investment policies than
mutual funds.
Idea: sophisticated/wealthiest investors need less protection.
Broad term that encompasses funds that follow very different strategies and have different risk and
return profile.
Hedge fund strategies focused on absolute returns: they don’t care about performance to a
benchmark. Even if market falls, HF is expected to perform well.
HF vs Mutual fund.
Full spectrum investing.
Hedge fund performance (% return) have been declining in the last few years due to that markets
become more efficient and lot more competition (among HF’s).
Module 1.2: Hedge Fund Fees and Performance
Management fee + incentive fee based on performance.
Incentive fee can be modeled as call option. -> may encourage excessive risk taking by HF manager
(asymmetric payoff).
Or high water mark.
- If fund experiences losses, incentive fee only paid when it makes up for these losses ->
creates incentive to shut down fund after poor performance and simply start new fund.
Funds of funds
- Hedge funds that invest in other hedge funds
, - Little diversification if underlying HF follow similar strategies
- Usually 1% management fee and 10% incentive fee
- Fee of Fee pays incentive fee to each underlying HF
- Number of FoFs has dropped after 2008 due to high fees
This table suggests that the diversification benefits of hedge funds may be lower than many investors
anticipate, especially during recession periods.
Performance outlook: Time trends in alphas of HF’s
Because of its big successes, lots of other HF got started, so competition raised. More arbitrage
capital was being deployed. Anomalies have become smaller and markets became more efficient.
Another explanation, stronger regulations.
Finally, financial incentives have decreased due to the AUM. If a lot of AUM, 2% management fee
alone makes him already rich.
Number one reason for underperformance of HF = too many hedge funds chasing limited
opportunities to generate alpha. Secondly, central bank monetary policy.
Module 1.3: Hedge fund Strategies
1. Directional (Bets)
- Bets on the direction of financial or economic variables
- Examples: increase in S&P 500, decrease in interest rates, etc.
- Often based on fundamental investment approach
- Typically not market neutral (positive or negative exposure)
2. Non directional (arbitrage: but no free lunch!) not really risk free
- Exploit temporary misalignments in security valuations
- Often quantitative investment approach (data mining?)
- Buy on security and sell another (e.g. pairs trading)
- Strives to be market neutral
- Relative value vs convergence trades: for latter, convergence period is usually known (e.g.
expiration of futures contracts). Seek to explore for mispricing.
Hedge fund alphas and betas (i)
Why do we care about alphas and betas?
• No point to pay fee for beta exposure that you can get yourself through index fund or ETF ->
only pay for alpha!
• Allows to check if HF manager follows proclaimed strategy
• Investor can short market index (future/ETF) to remove market risk.
, In fact, you want to know betas w.r.t (with reference to) all passive strategies!
Caveat: even multi-factor models struggle to explain performance of hedge funds (low R^2)
Alpha Transfer (i)
• Portable alpha strategy earns beta in one asset and alpha in another, often implemented using
futures contracts -> futures overlay strategy.
• Goal: separate asset allocation (beta) from security selection (alpha)
• Steps:
1. Invest where you have skill and can find alpha. (e.g. Japanese small-caps)
2. Hedge systematic risk (beta) away to isolate alpha. (short Nikkei futures) -> perfect hedge
ensures that return you earn is risk-free rate + alpha
3. Establish exposure to desired asset class by using index futures or ETF
Module 1.4 Why Do/Did Hedge Funds Do So Well
Potential reasons for HF outperformance.
1. Skill. Best managers leave MF and start an HF to earn higher fee.
2. Investment flexibility (leverage, short selling, derivatives)
3. Fraud (insider trading, etc.)
4. Data issues (smoothing, backfilling, survivorship, etc.)
5. Risk (liquidity risk, tail risk, correlation risk)
6. Methodological issues (skewness, non-linearities)
Week 1. Introduction
What is a quantitative model?
Financial modeling refers to asset pricing, return prediction, portfolio optimization, risk
measurement.
Model classifications (i):
1.Empirical (data driven) vs. theoretical model
- Empirical model tries to describe underlying data generating process as good as possible: from data
to model
- Theoretical model makes testable predictions based on abstract reasoning and set of assumptions:
from theory to model.
2. Deterministic vs. probabilistic (stochastic) model
- Deterministic model does not have random/uncertain term -> e.g. CAPM
- Probabilistic model does have random/uncertain term -> e.g. regression
3. Discrete vs. continuous variables model
- Discrete variable can take only discrete (specific) values -> binominal tree
- Continuous variable can take any value within certain range -> BS model
4.Discrete vs. continuous time model
- Discrete time: value of variable can change at fixed points in time (binominal tree)
- Continuous time: value of variable can change at any point in time (BS model)
5.Cross-sectional vs. time-series vs. panel data model
- Cross-sectional: comparing multiple units (companies, stocks) at point in time
- Time-series: track one unit (company, stock, country) over time
- Panel: Track multiple units over multiple time periods.
Model optimization
Models often involve some type of optimization (max/min output var)
Two main approaches:
1. Analytical: use calculus to derive first-order condition and set to zero.
2. Numerical: use brute force approach (try many different value of input variables)
Model Simulation
Monte Carlo simulation is powerful computer-based technique used to analyze and account for
uncertainty in financial decision making.
Model Risk
“Potential loss institution may incur as consequence of decisions that are principally based on the
output of internal models, as a result of errors in the development, implementation, or use of such
models”.
Sources of model risk:
- Specification (design)
- Implementation: spreadsheet/programming flaws, wrong input, wrong cell reference.
- Application (scope) function creep (used for purposes it was not designed for),
misinterpretation of model outputs
, - Environment: time-varying parameters, relations break down (regime shifts)
Module 1.1: Introduction to hedge funds
What are hedge funds: A private investment pool, open to institutional or wealthy investors, that is
largely exempt from SEC regulation and can pursue more speculative investment policies than
mutual funds.
Idea: sophisticated/wealthiest investors need less protection.
Broad term that encompasses funds that follow very different strategies and have different risk and
return profile.
Hedge fund strategies focused on absolute returns: they don’t care about performance to a
benchmark. Even if market falls, HF is expected to perform well.
HF vs Mutual fund.
Full spectrum investing.
Hedge fund performance (% return) have been declining in the last few years due to that markets
become more efficient and lot more competition (among HF’s).
Module 1.2: Hedge Fund Fees and Performance
Management fee + incentive fee based on performance.
Incentive fee can be modeled as call option. -> may encourage excessive risk taking by HF manager
(asymmetric payoff).
Or high water mark.
- If fund experiences losses, incentive fee only paid when it makes up for these losses ->
creates incentive to shut down fund after poor performance and simply start new fund.
Funds of funds
- Hedge funds that invest in other hedge funds
, - Little diversification if underlying HF follow similar strategies
- Usually 1% management fee and 10% incentive fee
- Fee of Fee pays incentive fee to each underlying HF
- Number of FoFs has dropped after 2008 due to high fees
This table suggests that the diversification benefits of hedge funds may be lower than many investors
anticipate, especially during recession periods.
Performance outlook: Time trends in alphas of HF’s
Because of its big successes, lots of other HF got started, so competition raised. More arbitrage
capital was being deployed. Anomalies have become smaller and markets became more efficient.
Another explanation, stronger regulations.
Finally, financial incentives have decreased due to the AUM. If a lot of AUM, 2% management fee
alone makes him already rich.
Number one reason for underperformance of HF = too many hedge funds chasing limited
opportunities to generate alpha. Secondly, central bank monetary policy.
Module 1.3: Hedge fund Strategies
1. Directional (Bets)
- Bets on the direction of financial or economic variables
- Examples: increase in S&P 500, decrease in interest rates, etc.
- Often based on fundamental investment approach
- Typically not market neutral (positive or negative exposure)
2. Non directional (arbitrage: but no free lunch!) not really risk free
- Exploit temporary misalignments in security valuations
- Often quantitative investment approach (data mining?)
- Buy on security and sell another (e.g. pairs trading)
- Strives to be market neutral
- Relative value vs convergence trades: for latter, convergence period is usually known (e.g.
expiration of futures contracts). Seek to explore for mispricing.
Hedge fund alphas and betas (i)
Why do we care about alphas and betas?
• No point to pay fee for beta exposure that you can get yourself through index fund or ETF ->
only pay for alpha!
• Allows to check if HF manager follows proclaimed strategy
• Investor can short market index (future/ETF) to remove market risk.
, In fact, you want to know betas w.r.t (with reference to) all passive strategies!
Caveat: even multi-factor models struggle to explain performance of hedge funds (low R^2)
Alpha Transfer (i)
• Portable alpha strategy earns beta in one asset and alpha in another, often implemented using
futures contracts -> futures overlay strategy.
• Goal: separate asset allocation (beta) from security selection (alpha)
• Steps:
1. Invest where you have skill and can find alpha. (e.g. Japanese small-caps)
2. Hedge systematic risk (beta) away to isolate alpha. (short Nikkei futures) -> perfect hedge
ensures that return you earn is risk-free rate + alpha
3. Establish exposure to desired asset class by using index futures or ETF
Module 1.4 Why Do/Did Hedge Funds Do So Well
Potential reasons for HF outperformance.
1. Skill. Best managers leave MF and start an HF to earn higher fee.
2. Investment flexibility (leverage, short selling, derivatives)
3. Fraud (insider trading, etc.)
4. Data issues (smoothing, backfilling, survivorship, etc.)
5. Risk (liquidity risk, tail risk, correlation risk)
6. Methodological issues (skewness, non-linearities)
