Time-Varying Volatility Financial Markets, Day 2, Class 2 Jun Pan - PowerPoint PPT Presentation

Time-Varying Volatility Financial Markets, Day 2, Class 2 Jun Pan Shanghai Advanced Institute of Finance (SAIF) Shanghai Jiao Tong University April 19, 2019 Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 1 / 54

Outline Volatility models and market risk measurement. Estimating volatility using fjnancial time series: EWMA for covariances and correlations. Portfolio volatility and Value-at-Risk. Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 2 / 54 ▶ SMA: simple moving average model (traditional approach). ▶ EWMA: exponentially weighted moving average model (RiskMetrics). ▶ ARCH and GARCH models (Nobel Prize).

The Aggregate Stock Market and the dividend-to-price ratio has some predictability for future stock Jun Pan Time-Varying Volatility Financial Markets, Day 2, Class 2 (low R-squared’s), and much of the uncertainty is unpredictable. Overall, only a small portion of future stock returns can be predicted returns. The autocorrelation of the aggregate stock returns is slightly positive, It is pervasive, the single most important risk factor in the equity There is some evidence that the expected returns are time varying. measure with precision because of It yields a positive risk premium, but the risk premium is diffjcult to world. 3 / 54 ▶ the “high” level of stock market volatility ▶ and the limited length of the historical data.

The Volatility of the Aggregate Stock Market Historical data can be used to measure volatility with much better Jun Pan Time-Varying Volatility Financial Markets, Day 2, Class 2 We will study three volatility estimators: practitioners have adopted many of the ideas developed by academics. Academics have made much progress in both directions, and derivatives prices (forward looking). historical stock market data (backward looking), but also from In fact, we can learn about market volatility not only from the more information about. precision. Between risk and return, risk is something we can collect 4 / 54 ▶ SMA: simple moving average model (traditional approach). ▶ EWMA: exponentially weighted moving average model (RiskMetrics). ▶ ARCH and GARCH models (Nobel Prize).

The Importance of Measuring Market Volatility Portfolio managers performing optimal asset allocation. Risk managers assessing portfolio risk (e.g., Value-at-Risk). Derivatives investors trading non-linear contracts with values linked directly to market volatility. Increasingly, the level of market volatility (e.g., VIX) has become a market indicator (“the fear gauge”) watched closely by almost all institutional investors, including those who are not trading directly in the U.S. equity or U.S. equity derivatives markets. Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 5 / 54

Modern Finance Financial Markets, Day 2, Class 2 Jun Pan Time-Varying Volatility 6 / 54 4 2 0 0 1 9 Mortgage 0 6 1 9 8 2 0 9 5 0 1 5 1 First Stock 2 8 9 9 2 1 Backed 3 1 9 Investments and Index Futures 8 0 9 0 1 8 3 0 6 Securities 0 Capital Structure 5 6 1 0 2 1 9 (Fannie (Modigliani and Miller) 8 9 2 2 1 1 Two-Fund 19 WorldCom 8 0 9 Mae) 0 7 4 0 Financial 6 0 Separation Scandal 5 7 79 2 2 1 Crisis 9 (Tobin) 9 2 19 01 1 Enron 9 85 0 OTC Derivatives 1 6 0 6 20 Scandal 5 8 3 19 8 Interest 1 19 7 9 2 0 9 Rate 8 00 CAPM Rise of Dot-Com 0 1 55 6 1 64 1 Swaps 0 (Sharpe) Junk Bonds Peak 9 20 77 2 19 987 1 (Michael Stock 1998 1999 9 Dodd-Frank 9 Efficient Markets 4 1 Milken) 10 20 6 Market 5 5 Hypothesis 6 9 Index Mutual 7 Crash 988 1 LTCM European 3 1 19 (Samuelson, Fama) 9 Funds (Bogle) 1 1 Crisis Sovereign 66 5 1 9 5 19 S&L Bailout Crisis 7 01 9 2 1 7 9 Asian 8 01 Collapse of 9 9 1 2 52 9 6 9 Crisis 4 2 8 7 Junk Bonds 1 Trade 1 9 7 1 9 2 51 1 1 7 9 First Credit 0 War 90 0 9 Mutual Funds 1 99 2 Portfolio 6 1 3 TIPS Derivatives 8 Study (Jensen) 7 3 7 1 Theory 0 19 1 9 1 1 First US Options (CDS) 1 9 2 6 9 0 (Markowitz) 3 9 0 9 6 7 Exchange, CBOE Chinese 2 9 1 1 9 9 95 1 4 1 6 2 1 9 7 1 9 Stock 7 2 1 0 1 Option Pricing Theory 1 7 1 9 1 9 5 0 0 Trump 1 9 2 9 Market 5 (Black, Scholes, Merton) Birth of Index 2 9 1 1 Crash Funds (McQuown) 9 4 9 9 3 9 1 Large Derivatives Losses

The Evolution of an Investment Bank Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 7 / 54

Derivatives Losses by Non-Financial Corporations in 1990s Dell Computer: $35 million, leveraged interest rate swaps Jun Pan Time-Varying Volatility Financial Markets, Day 2, Class 2 Mead: $12 million, leveraged interest rate swaps Gibson Greetings: $20 million, leveraged interest rate swaps Arco Employees Savings: $22 million, money market derivatives Louisiana State Retirees: $25 million, IOs/POs currency swaps Orange County: $1.7 billion, leverage (reverse repos) and structured Air Products & Chemicals: $113 million, leveraged interest rate and Proctor & Gamble: $157 million, leveraged currency swaps Codelco: $200 million, metal derivatives Barings: $1 billion, equity and interest rate futures Metallgesellschaft: $1.3 billion, oil futures Showa Shell Sekiyu: $1.6 billion, currency derivatives notes 8 / 54

Measuring Market Risk fjnancial assets, constitute the key inputs to Value-at-Risk. JP Jun Pan Time-Varying Volatility Financial Markets, Day 2, Class 2 matrix of 480x480. 480 fjnancial time series in order to construct a variance-covariance (EWMA) model to estimate the volatilities and correlations of over Morgan’s RiskMetrics uses exponentially weighted moving average Daily estimates of market volatility, along with correlations across By the early 1990s, the increasing activity in securitization and the system. Street fjrms have developed risk measurement into a fjrm-wide communicated to the chief executives. By the mid-1990s, most Wall aggregate the fjrm-wide risk to a set of numbers that can be easily Market risk management tools such as Value-at-Risk are ways to chief executives to understand the overall risk of their fjrms. books of many investment banks too complex and diverse for the increasing complexity in the fjnancial instruments made the trading 9 / 54

Equity Markets around the World Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 10 / 54

FX Markets Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 11 / 54

Money Market Rates Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 12 / 54

Government Bonds Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 13 / 54

Interest Rate Swaps Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 14 / 54

Commodities Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 15 / 54

Estimating Volatility using Financial Time Series SMA: simple moving average model (traditional approach). EWMA: exponentially weighted moving average model (RiskMetrics). ARCH and GARCH models (Nobel Prize). Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 16 / 54

Daily Returns on the S&P 500 Index Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 17 / 54

The Simple Moving Average Model Unlike expected returns, volatility can be measured with better Jun Pan Time-Varying Volatility Financial Markets, Day 2, Class 2 N N 18 / 54 micro-structure noises such as bid/ask bounce start to dominate in day return. The simple moving average (SMA) model: the intra-day domain. So let’s not go there in this class. precision using higher frequency data. So let’s use daily data. Some have gone into higher frequency by using intra-day data. But Suppose in month t , there are N trading days, with R n denoting n -th � � � 1 � ∑ ( R n ) 2 σ = n =1 √ To get an annualized number: σ × 252 . (252 trading days per year).

Financial Markets, Day 2, Class 2 the volatility calculation. Time-Varying Volatility Jun Pan 19 / 54 Whether or not to take out µ ? The industry convention is such that ( R t − µ ) 2 is replaced by R 2 t in The reason is that, at daily frequency, µ 2 is too small compared with E ( R 2 ) . Recall, µ is several basis points while σ is close to 1%. So instead of going through the trouble of doing E ( R 2 ) − µ 2 , people just do E ( R 2 ) .

Volatility Estimated using SMA model Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 20 / 54

How Precise are the SMA Volatility Estimates? Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 21 / 54

What about SMA Mean Estimates? Financial Markets, Day 2, Class 2 Time-Varying Volatility Jun Pan 22 / 54