Beta Weighted Risk Navigator Webinar Notes

Overview

Our enhanced Risk Navigator application within Trader Workstation now provides Beta-weighted metrics. This allows a portfolio manager to consider possible profit and loss scenarios for a universe of stocks with respect to an underlying reference contract such as the S&P 500 index or any other contract of choice. Because individual stocks perform differently over time in relation to the broad market, using historic data to calculate correlations between individual stocks and benchmarks allows the investor to understand the net sensitivity of his portfolio to the broad market. First to ensure that your Risk Navigator will pull-in Beta metrics, you should put a check next to the Beta Weighted Portfolio selection under the View menu inside of Risk Navigator. The first time you do this, you may be asked to select your reference index, which by default is the S&P 500 index. This can be changed at any time later if you wish to consider portfolios made up of foreign stocks or want to choose an alternative US index or even an individual stock.


Portfolio Theory

The concept of beta was adopted in the formulation of the Capital Asset Pricing Model (CAPM), which is the cornerstone of modern portfolio theory. CAPM is used to estimate the expected return on an asset during a specific timeframe in terms of the risk of return. CAPM is, therefore, used to calculate the cost of equity. When approaching single security analysis, investors generally recognize systematic and nonsystematic risk.

Systematic risk or market risk uses the concept that stocks move up or down broadly in-line with the broad market. Market or systematic risk cannot be diversified away, but nonsystematic risk, or the risk associated with investing in a single stock in isolation, can be diversified by investing in an array of securities. The underlying concept of beta is that it is a means to characterize the historic relationship between an individual security and the broad market.

Before we focus on Beta-metrics added to IB Risk Navigator, I would like to point to a new method for measuring country risk using Risk by Country report, which groups risk by geographic location. Using this report, it is possible to view equity exposure by country of origin. At the highest order, investments are grouped by continent and then by country.


Chart – Risk by Country

Beta-Weighted Risk Navigator

So for example, shares of US companies would fit under North America and then United States. ADR shares of Chinese Internet company Baidu Inc. (Ticker: BIDU), listed on NYSE and priced in US dollars, would display under Asia and China within this report. US-listed shares you might own in in European banks, for example, and held as part of your US dollar portfolio, would display under Europe and Germany. This allows you to display using the Country Report, exposure by region, in which you can further drill down to display as a percentage of your net liquidation value of NLV.

In order to see Beta risk enhancements in TWS, users will need to be running version 947 released in October 2014. Users can now add a variety of Beta-related risk metrics in both Plot and Report views. In order to see Beta-weighted values in the plot format, users must first place a check mark next to the Beta Weighted Portfolio from the View menu. For reports, users need only select required Beta-metrics from the Metrics and Beta Risk menus.


Why the Enhancements

Portfolio risk managers like to see various measures of risk and because some products are more or less sensitive than others to the broad market, it was a natural addition to add Beta values. They are also aware of past returns or how stock prices have moved relative to a benchmark and be prepared for the future by thinking about expected returns.


  • For example, a stock's daily return is its price change for the day divided by its price on the previous close
  • The expected rate of return for a stock is its beta times the return of the reference index over some time period

So when considering the outlook for a portfolio, think about how we could contrast the plot under two scenarios

    • Equal-weight – An equal-weighted plot assumes that ALL stocks have the same daily rate of return
    • Beta-weight – A beta-weighted plot assumes that EACH stock moves by the amount predicted by its historical beta versus the selected market index
    • An equal-weighted plot most accurately represents when the market moves as a whole, such as a large market dislocation
    • A beta-weighted plot better reflects the day-to-day statistical variation of the market prices

Adjusting Reference Contracts and Beta Calculations

As noted earlier, beta measures the sensitivity of a security to an underlying benchmark such as a stock index. Users can change both benchmark reference contracts and the beta calculation method using the Risk Navigator. Beta calculations are made from daily returns over the past two-years. To change time horizon or select from frequencies of daily, weekly or monthly returns, use the Edit menu and choose the Beta Calculation Method.

Selected Reference Contract – This can be any individual stock or available index, and can be changed at any time. Use the Settings menu and select from available items in the Beta Reference index selector, or type in your chosen stock symbol. Alternatively, click on the status bar named Beta Reference beneath the plot area and select your own or from the list of global indices.


Chart – Global Setting for Plot view

One way to explain the benefits of using the Beta-weighted metrics within Risk Navigator is to devise a portfolio of relatively high and relatively low beta names, investing an approximately equal amount in each. Users can work within their existing portfolio to add any of the columns we will discuss throughout this session. However, it is also possible to replicate your portfolio or construct a What-if portfolio from the Portfolio menu and selecting New as your option. You will be prompted to set-up a new portfolio with or without your existing portfolio. You should note that within the What-if portfolio it is possible to use the include/exclude feature, which efficiently allows you to check a box to incorporate or exclude positions such that you can immediately see the impact on risk arising from each position. The include/exclude feature is only available in What-if portfolios. Likewise it is not possible to add positions to real portfolios.

Beta-Weighted Risk Navigator

Chart – Insert Beta, Weight and Weighted Beta from Metrics and Beta Risk menu

Beta-Weighted Risk Navigator

As you work through the IB Risk Navigator, please be aware that there are many different reports available. Please note that in order to see aggregated column values across the top of a report you must select the report called Risk by Underlying from the report viewing area of the page. The Aggregation value row for all-metrics is not viewable within the Portfolio report.

You can see from the Weight column that the dollar amount is roughly equal in this case. Notice too that the display is sortable by any column. The column sort we want in this case is by Beta value in descending order, which you will see is denoted by the red-down arrow (chart below). Beta values are calculated by default using two-year history. Both reference index, such as the S&P 500 index, and the Beta period setting can be changed from the Edit menu (must specify later in the piece). Stocks that are sensitive to the performance of the reference benchmark have a high Beta, while stocks that move relatively less have a low Beta. Betas calculated by the system are automatically displayed (in a black font) in Risk Navigator and when manually altered, they are displayed in red.

By displaying the portfolio according to a high-to-low Beta sort, you will also be able to contrast the dollar weight to the Weighted Beta reading. The raw Beta reading describes the under or over performance of the stock to the index. A Beta of 1.0 implies that the stock moves exactly in line with the index. A stock with a beta of 2.0 both rises and falls with two-times the return of the index. More specifically, the stock's return historically is the same as the return of the index. A Beta reading of 0.5 infers that the stock rises or falls at half the return of the index over time. Based upon the raw Beta readings, the Risk Navigator computes the Weighted Beta for each component of the portfolio. This reading considers the weight of the stock in the portfolio and the sensitivity of the stock to movement both up and down in relationship to that of the index over time. So higher Beta stocks carry greater weight. Notice that at the top right of your Risk Dashboard (enabled by placing a check next to Risk Dashboard from the View menu), the Average and Portfolio Beta values are calculated. The Average Beta is a simple, straight sum of stock Betas divided by the number of positions, while Portfolio Beta is weighted by position. If the portfolio consists of Delta-one assets then one expects the return of the portfolio to be Portfolio Beta times the return of the index.

The index delta column (in which the chosen index is named) converts the position in each underlying into the equivalent number of shares of the index. The total index delta is shown in the All Underlyings line tells the number of shares of the index the portfolio effectively represents. It is particularly useful since one can establish a position in the index of the total delta size with the opposite sign to immediately hedge the market risk of the portfolio.


Chart – Default Beta is calculated per stock and for relative portfolio weighting

Beta-Weighted Risk Navigator

The difference in aggregation is displayed using the plot function. Remember that at the Portfolio level, using the Report Viewer, the resulting plot displays the expected portfolio value change for a given change in the value of the respective index. Notice at the top of the chart, and assuming you have enabled the Beta Weighted Portfolio from the View dropdown menu, you should be able to see a dropdown menu from which you can select either Beta Weighted or Equal Percentage Move Aggregation. This is where the real contrast becomes apparent for your portfolio depending on which measure you use. The Equal Percentage method will calculate the expected impact on the Portfolio should the reference index move up or down using the Weight of each stock. By contrast, the Beta Weighting projects expected profit and loss given the composition of stocks and their historic performance relative to the benchmark. The value of the x-axis can be changed manually by clicking on the status bar beneath the plot allowing users to toggle between the percentage price change for the reference contract or actual prices.

Chart – Plot using equal percentage move aggregation versus Beta weighted

Beta-Weighted Risk Navigator

We could compare two portfolios – the first with high beta names and the other comprised with stocks showing relatively low Betas. To check this, we can hold the crosshair at a +5% move for each and compare the expected portfolio value in the base currency. When the portfolio Beta is greater than 1.0, we would expect to see a steeper upwards sloped curve. By contrasting the high and low Beta portfolios we can prove that the gradient is steeper for the portfolio with a higher overall Beta. To display this, select the crosshair tool from the View dropdown menu and place on the plot at exactly the 5% change reading. You should notice that the estimated portfolio value change is greater for the high Beta portfolio. To confirm the concept look at the dollar value from the y-axis and read off what percentage change in the underlying market index would be required to impact each portfolio by the same amount.

Chart – Contrast the Beta-Weighted Plot for high and low Beta portfolios assuming 5% index increase

Beta-Weighted Risk Navigator Beta-Weighted Risk Navigator

So now let's consider what might happen to a small portfolio in the event that the market moves. We are interested in understanding the value change in the portfolio under each Beta-weighted and equal-weighted scenario. Let's drill down into the previous concept further by building a new What-if portfolio of just two stocks – IBM (Ticker: IBM) and Microsoft (Ticker: MSFT). Note that it is possible to edit the Beta value by simply typing in each field under the beta column with your own value. Red-font will populate to denote user-input values, while black-font shows system-generated Betas. By assigning a 0.5 Beta for IBM and a 1.5 Beta value for Microsoft, we can contrast the impact on a portfolio and at the individual level at the equal-weighted and Beta-weighted level. Regardless of the number of shares we purchase in each stock, the average Beta of the portfolio will be 1.0.

The portfolio value change for an index move in equal-weighted portfolio…

Beta-Weighted Risk Navigator

Assumes same percentage change for all portfolio holdings

Beta-Weighted Risk Navigator

Beta-Weighted Risk Navigator

With the Report Viewer set to All Underlyings, select Equal Percentage from the toggle bar at the top of the plot. The x-axis displays percentage change in the value of the underlying index and the y-axis shows the impact on the portfolio in base currency terms. Here we are looking at the expected change in portfolio value as the reference index changes. For a 10% increase in the reference index, compare the expected portfolio value change for equal-weight and then toggle to the Beta-weighted setting to see the difference. Note what happens to the value of the currency range as you toggle between equal and Beta-weighted portfolios.

Look at the impact of a 10% increase in the value of the underlying and how it is reflected in the dollar gain at 10% for all underlyings. The Risk Navigator assumes a synchronous increase of 10% for both MSFT and IBM. So we can check this by toggling to each individual underlying and measuring the value at a 10% gain. The sum of gains for each should equal the rise in the value of the Equal Weighted plot.

Now, if we shift gears to the Beta-weighted plot look to the dollar impact of a 10% gain in the underlying index. It should be different to the assumed equal-weighted change. The Beta-weighted portfolio value change assumes that each stock rose according to its Beta, such that IBM added 5% for a 10% gain in the index, while MSFT rose by 15% for the same change in the reference benchmark. If we toggle to each underlying and measure the currency/dollar gain for each by using the crosshair, we should be able to reconcile the Beta-weighted gain and the different pace of increase in the two underlying stocks.


The portfolio value change for an index move in beta-weighted portfolio…

Beta-Weighted Risk Navigator

Assumes individual components shift by the value of their Beta relative to percentage change for reference index

Beta-Weighted Risk Navigator Beta-Weighted Risk Navigator

Adding option positions

Users can add option positions to Risk Navigator either by click-and-dragging from TWS, or simply by typing in to the NEW underlying column and adding the number of desired contracts. Note that Risk Navigator will compute Greek values for options as usual and add various Beta-related metrics, but will only display Beta values for the underlying security. Weighted-Beta readings will appear.


Chart – Notice there is no Beta value calculated for option positions

Beta-Weighted Risk Navigator

Adding Beta variables

So far we have limited the number of Beta-related variables in order to explain the concept as an addition to IB Risk Navigator. However, there are additional fields that can be added to the Risk Navigator. First, from the View menu ensure you have the Beta Weighted Portfolio checked. This ensures evaluations and plot data are calculated and displayed. Second, from the Metrics dropdown, use the Beta Risk tree menu to select from a total of nine different column metrics. Investors can view Beta Delta, Beta Delta Dollars and also as a percentage of net liquidation value (NLV). The same variables are available for the reference underlying index such as SPX for the S&P 500 index or RYO for the Russell 2000 index and so on. So if you change the Beta Reference Index from the Settings dropdown menu, the display for Delta Dollars changes accordingly.


Chart – Beta variable display changes according to which reference index is chosen

Beta-Weighted Risk Navigator
Beta-Weighted Risk Navigator

Remember that, for help with any column definition, hold your mouse over the column-header for pop-up description. For full description of all Beta Weighting fields displayed in IB Risk Navigator, please see this link.


Using Beta-metrics for Portfolio Hedging

The concept of Beta allows us to consider that different portfolios might react faster or slower than a commonly used benchmark. That notion has implications for portfolio hedging. For portfolios with higher-values for Beta, we can measure the Beta-weighted delta dollar equivalent with respect to the chosen reference index. We also need a hedging tool, which for the S&P 500 we could choose the SPDR S&P 500 Trust ETF (Ticker: SPY) and/or put options on the same fund. In order to hedge a stock portfolio with the short-sale of shares in the ETF, look at the value of the Beta-weighted delta dollar column (available through the Metrics, View and Beta risk tree). You will notice that since the portfolio is high-beta, the short position required to hedge this overly-sensitive portfolio is higher than it would be if we were simply hedging with respect to the Delta dollar value.


Chart – Hedging Beta-weighted delta dollar values with SPY ETF

Beta-Weighted Risk Navigator

Use the New field under the All underlyings column to generate line items for the SPY and perhaps a put option. Compare values for the SPY delta dollar reading for all underlyings and compare to that for Beta-weighted delta dollars. For hedging purposes, you can estimate the number of shares required to reduce the value of Beta-weighted delta dollars to zero. Before you type in a number of shares to hedge using SPY, look at the expected portfolio value change for a 10% change in the reference index. Add the appropriate offsetting SPY position to your portfolio, sufficient to drive the BWDD position to zero and then check on the updated plot the impact of a 10% change in the reference index. The hedge should reduce the expected swing.

You can include and exclude the position quickly in order to compare the impact of the hedge. If we exclude the ETF hedge and focus only on hedging with options instead, we can find the appropriate number of put options to drive the Beta delta dollar value towards zero. Note this time that the Plot shows a better symmetry than did the short ETF position. Note also the impact of a 10% change both up and down in the expected portfolio value once the put options are included.


Chart – Comparing Delta dollars, SPY Delta dollars and Beta-delta dollar values with SPY options

Beta-Weighted Risk Navigator

Additional Fields

We should also bring your attention to several enhancements that have been added to the Risk Navigator that maybe useful to you depending on your trading style. Columns can be added to review the long or short value of your portfolio and its component pieces. And don't forget that you can sort your display in any report by any of the available column headers just by clicking on the field header. We have also added a field calculating how long it would take to dispose of either a large or illiquid position from your portfolio. See under Metrics>Value menu for "days to liquidate". On the same theme, we have added a field for the percentage of your positions that can be liquidated in 3/5 and 10 days. Finally, you can now view fields for Gross Value and Gross Value as a percentage of Net Liquidation Value.