Agent-based models of financial markets

Examples of different models

October 3, 2016

Seminar Overview

• September 19: Introduction and basic concepts

• September 26: Financial markets and ABM

• October 3: Examples of different models

• October 10: Introduction to the development framework

• October 17: Scenario analysis and simulation

• October 24: The agents’ behavior (Guest speaker Faten Ben Bouheni)

• October 31: Implementation of agents’ behavior

• November 7: Evolution and learning

• November 14: Optimization and overfitting

• November 21: Commercialization of models / How to pitch (Guest speaker Roger Hilty)

• November 28: Pitch of the models

• December 5: Pitch of the models

• December 12: Pitch of the models

• December 19: General feedback to the pitch sessions and some conclusions

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Content

• Switzerland’s real estate market

• Real estate cycles

• A model of the Swiss real estate market

• A model of the Swiss real estate stocks

• A Model of the Swiss stock market

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Volume of Swiss real estate market 2014 (bn CHF)

www.avaco.ch Source KRE-KloessRealEstate, Wüest&Partner, pom+, HEV, CreditSuisse

Swiss real estate market

• Construction volume 2013: CHF 32.5 bn

• Reconstruction volume 2013: CHF 15.1 bn

• Annual transaction volume privat: CHF 30 bn

• Annual transaction volume institutional: CHF 20 bn

• Europe’s lowest homeownership rate (36.8% in 2011), high share of rented homes. However, share of homeownership is raising. Yet, stagnation on a higher level?

• Interest rates at a historical low. Swiss National Bank (SNB) keeps interest rates close to zero. Limited monetary policy instruments due to appreciation pressure of CHF.

www.avaco.ch Source KRE-KloessRealEstate, Wüest&Partner, pom+, HEV, CreditSuisse

Total return development

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Total return versus price index

www.avaco.ch www.six-swiss-exchange.com/indices/data_centre/other/iazi_en.html

www.avaco.ch www.six-swiss-exchange.com/indices/data_centre/other/iazi_en.html

Is it important?

• The Swiss real estate market is attracting much attention at the moment. Increasing concerns about overheating and corresponding correction.

• Weakening demand in view of constricted incomes, more restrictive funding, high prices, less immigration.

• Past years’ rising prices led to high returns for investors and little defaults for creditors. However, important risks for most investors are real estate (equity or debt capital) and interest rate risks. Use of leverage (mortgages) increases this effect.

• Established real estate management practice (particularly credit risk management) focuses on individual business case during acquisition phase and takes bottom-up perspective.

• Illiquidity and high transaction costs.• Cyclical price formation.

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Real estate cycles 1971-2007

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Detrended real estate prices according to calculations by Agnello and Schuknecht (2009) in 1971-2007 for different countries. In red: Ratio of amplitude (vertical line) to duration (horizontal line) of a real estate cycle. In blue: Real estate cycles which were still continuing at the end of 2007 (see next slide).

Source: Agnello L., Schuknecht L. (2009): Booms and Busts in Housing Markets – Determinants and Implications. Working Paper published by the European Central Bank (ECB). No. 1071. http://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp1071.pdf (For increased understandability the original figure as published by Agnello and Schuknecht has been modified by us.)

Real estate cycles 1993-2013

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• Real estate prices are subject to strong cyclical fluctuations.

• Prices are usually either rising or falling; prolonged sideways movements rarely occur.

• Strong correlation between times of decreasing prices and times of increasing prices: Price decreases and increases have roughly the same duration.

Source: BIS (2013): Property Price Statistics. Bank for International Settlements (BIS). http://www.bis.org/statistics/pp.htm (The data were pre-processed and detrended applying the same procedure as Agnello and Schuknecht.)

Swiss real estate cycle

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Source: Own calculations and http://www.iazicifi.ch/de/swx-iazi-investment-real-estate-price-index.php

If the downturn phase mirrors the preceding upturn phase, and assuming that the cycle’s tipping point is reached today, both indices can be projected into the future.

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'87 '89 '91 '93 '95 '97 '99 '01 '03 '05 '07 '09 '11 '13 '15 '17 '19

Real Estate Price Indices and Forecast (Assuming Constant Interest Rates)

SI Investment PR Forecast

What are the elements?

• Who are the relevant market participants?

• What are the decision rules of the market participants (agents)?

Please take five 5 minutes to think about this question.

Briefly prepare for a discussion in class - discuss it with yourneighbours.

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OrderOrder

Market

Order

Trend followers

Private residents

Investors

BUY!

SELL!

Real estate pricesInvestment

OrderOrder

Order

OrderOrder

Order

Real estate pricesPrivate

Rental fees

Interest rates

Stocks

Population

Model of the Swiss real estate market

ABM of the Swiss real estate market (1)

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Model Switzerland (v3)

Agent classes • Private residents• Institutional investors• Trend follower/Speculators (1 per market)

Traded goods/markets • SWX IAZI Investment Real Estate Price Index (SI Investment PR)• SWX IAZI Private Real Estate Price Index (SI Private PR)

Initial values • Private residents:Cash: 200’000 CHFPortfolio IAZI Private PR: 2.0

• Institutional investor:Cash: 100’000 CHFPortfolio IAZI Investment PR: 1.0

• Trend follower 1 (Investment):Cash: 100’000 CHFPortfolio IAZI Investment PR: 1.0

• Trend follower 2 (Private):Cash: 100’000 CHFPortfolio IAZI Private PR: 1.0

Input decision factors (time series) • SI Investment PR• SI Private PR• Swiss Bond Index• MSCI World Index• Swiss rental price index• Population

Decision rules • For private residents and trend followers:If COUNT(B) > COUNT(S) BUYIf COUNT(B) < COUNT(S) SELLIf COUNT(B) = COUNT(S) NO_ACTION

• For institutional investors:If (COUNT(B) - COUNT(S)) > 1 BUYIf (COUNT(B) - COUNT(S)) < -1 SELLIf -1 < (COUNT(B) - COUNT(S)) < 1 NO_ACTION

ABM of the Swiss real estate market (2)

Input decision factors/time series per agent class:

www.avaco.chB = Buy-Indicator, S = Sell-Indicator, X = No Action-Indicator

Input decision factor per agent class

Institutional Investors Private residents Trend followers(SI Investment PR)

Trend followers(SI Private PR)

SI Investment PR B, if trend ↗S, if trend ↘X, if trend →

- B, if trend ↗S, if trend ↘X, if trend →

-

SI Private PR - B, if trend ↗S, if trend ↘X, if trend →

- B, if trend ↗S, if trend ↘X, if trend →

Swiss rental price index B, if trend ↗S, if trend ↘X, if trend →

B, if trend ↗S, if trend ↘X, if trend →

- -

Swiss Bond Index B, if trend ↘S, if trend ↗X, if trend →

B, if trend ↘S, if trend ↗X, if trend →

- -

MSCI World Index B, if trend ↘S, if trend ↗X, if trend →

- - -

Population B, if trend ↗S, if trend ↘X, if trend →

ABM of the Swiss real estate market (3)

• No individual learning of the agents

• Social learning• Buy order using up 10% of the agent’s cash position.• Sell order worth's 10% of the agent’s real estate portfolio.

• The accumulation (loss) of wealth increases (decreases) the influence of an agent’s orders on the model signals.

• Market Maker (round based)

• The price calculation is based on demand and supply:

𝒚𝒕+𝟏 = 𝒑𝒕 + 𝜶𝒑𝒕𝑫 𝒕 − 𝑺(𝒕)

𝑫 𝒕 + 𝑺(𝒕)

p is the time series and y is the predicted time series; D is demand and S is supply of all agents

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Quality measure to access the forecasting quality: i) Hit Rate

• Hit = correct prediction of target measure movement

• Miss = inverted prediction of target measure movement

• No_Activity = no prediction, because trading signal < signal threshold

Hit Rate: ℎ =𝑛ℎ𝑖𝑡𝑠

𝑛ℎ𝑖𝑡𝑠+𝑛𝑚𝑖𝑠𝑠𝑒𝑠+𝑛𝑛𝑜_𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦

The hit rate indicates how often an up or down movement in price has been correctly predicted. Its values are between 1 (100% hits and 0% misses) and 0 (0% hits and 100% misses). If h = 0.5 (50% hits and 50% misses) then hits and misses cancel each other. Consequently, the model is not better than a random predictor (flipping a coin).

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Hit Rate

Quality measure to access the forecasting quality: ii) Model Efficiency

Model efficiency: 𝑟 = 𝑖=0𝑛 𝑠𝑡 𝑝𝑡+1−𝑝𝑡 𝑖=0𝑛 𝑝𝑡+1−𝑝𝑡

, with

𝑠𝑡 = 1 = 𝑏𝑢𝑦𝑠𝑡 = −1 = 𝑠𝑒𝑙𝑙

𝑠𝑡 = 0 = 𝑛𝑜 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦

Although the hit rate gives an overall impression of the number of correctly predicted price movements, it does not say anything about the relative size of these movements and the resulting potential gains and losses. As is well known, a single big drawdown can nullify a whole series of precedent gains. The model efficiency can have values between -1 and 1. If its value is 1 (-1), all possible gains (losses) through correctly (wrongly) predicting up and down movements of the target measure are realized by trading according to the model’s predictions. If it is 0, the gains equal the losses and the model is not better than a random predictor (flipping a coin).

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Model Efficiency

Quality measure to access the forecasting quality: iii) Performance

Performance: 𝑞 = 𝑖=0𝑛 𝑠𝑡 𝑝𝑡+1 − 𝑝𝑡 , with

𝑠𝑡 = 1 = 𝑏𝑢𝑦𝑠𝑡 = −1 = 𝑠𝑒𝑙𝑙

𝑠𝑡 = 0 = 𝑛𝑜 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦

The performance measure is similar to the model efficiency. It expresses the gains through trading price movements not relatively but absolutely. It has the same unit as the prices (e.g. CHF).

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Performance

ABM of SI Investment PR index

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The chart shows the development of the SI Investment PR index and the BUY-/SELL-signals generated by the model

Hit Rate: h = 0.76Model Efficiency: r = 0.56(June 30, 2016)

ABM of SI Private PR index

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The chart shows the development of the SI Private PR index and the BUY-/SELL-signals generated by the model

Hit Rate: h = 0.75Model Efficiency: r = 0.55(June 30, 2016)

Scenario Analysis

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«Nil-scenario»

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SI Investment PR

Key points!

• The AVACO model of the Swiss real estate market fits the development of the market since 1986 well.

• Hit Rate and Model Efficiency are high, however……the target time series has a low volatility.…the target time series is in some parts interpolated.

• The model is simple, yet can effectively be used by investors to test investment strategies and by risk managers. Useful for forecasting (investment strategy) and simulation (scenario analysis, e.g. herding and crashes).

• Model relies on both fundamental and technical factors.

• The model combines implicit and explicit knowledge.

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A model of the Swiss real estate stocks

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SXI Swiss Real Estate Shares

The SXI Swiss Real Estate Shares subindex contains the 5 most liquid and highly capitalized issues of the SXI Real Estate Shares universe. A security is included in the SXI Swiss Real Estate Shares subindex if it is ranked 5th or better in the related selection list. In addition, a SXI Swiss Real Estate Shares candidate must have at least 75% of its assets invested in Switzerland.

www.avaco.ch www.six-swiss-exchange.com/indices/data_centre/shares/sxi_realswissshares_en.html

Asset universe

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JPY

USD

CHF

EUR

Gold

Nikkei Bond

S&P

Oil

Bond Bond

DAX

BondSPI

Real Estate

Model

• Monthly model

• Two type of agents• Trend follower with 6 month time lag

• Investor compares the real estate stocks against the SPI

• Hit rate: h = 0.57

• Model efficiency: r = 0.33

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Performance

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Swiss Performance Index

• Monthly model

• Two type of agents• Trend follower with 3 month time lag

• Investor compares the real estate stocks against the EUR-CHF

• Hit rate: h = 0.61

• Model efficiency: r = 0.27

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Swiss Performance Index

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Readings

Kostadinov, F., Ankenbrand, T. (2013): Agent-based modelling and the Swiss real estate market. Working paper (available www.avaco.ch).

Kostadinov, F., Ankenbrand, T. (2013): Swiss Real Estate Market – IsSoft Landing an Option. Working paper (available www.avaco.ch).

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