# Main Exposure

The Main Exposure screen allows you to produce a variety of custom exposures on any portfolio loaded in SpanRM. In this view, the risk measures of the individual components of the portfolio are aggregated to measure the total portfolio risk exposure. Using the controls on the form, the user sets ranges and increments for the risk sensitivities he or she wishes to display in the matrix.

The Main Exposure screen can be accessed in one of two ways:

1) highlight the portfolio on the tree and click on the 'Analyze' button on the toolbar , or

2)right-click on the portfolio and choosing Analyze from the menu, as in Figure 1.2.

**Figure 1.2**

The user is presented with a screen like the one shown in Figure 1.3.

** Figure 1.3**

The data shown in the matrix (bottom portion of Figure 1.3) is what will be referred to as the 'exposure'. The exposure screen shows a portfolio's risk measures and dollar exposure to movements in the selected variable of the underlying contract. For example, Figure 1.3 shows different measures of the risk exposure in the price of the S&P500 futures contract. The controls on the top half of the window allow the user to customize the ranges and variables shown in the exposure.

The bolded column in the middle of the exposure indicates the settlement price or, if the price has been changed in the system, the last updated trade price of the underlying.

The price points to the left and to the right of the bolded column are the prices upon which each column's risk measures are based. The controls that are used to determine these increments and ranges will be explained in more detail in subsequent sections of this guide.

Rows in the Exposure

There are eight primary rows in the exposure:

__1) Underlying__:

Shows the quantity of the underlying product for the selected Combined Commodity.

**Filtering Underlying by Series**

When a portfolio contains multiple months, or 'Series', for a particular Combined Commodity, you can use the Product drop-down box to filter for a specific Product Series. (Figure 1.6)

Figure 1.6

The Underlying quantity row will display the quantity for that specific Product Series. After choosing a different Product series, you must recalculate by clicking 'Calculate Risk', or hit the enter key on your keyboard. This allows you to view the risk of the portfolio by individual quarterly expiration buckets independent of the total portfolio.

__2) Option Delta (Opt.Delta)__

This row displays the aggregate sum of the option deltas for the combined commodity being analyzed. The option delta shows the change in the value of the options for a change in the value of the underlying price. As you look across this row, you can see the change in the net delta as the price of the underlying changes. For example, in Figure 1.4, the net option delta at the futures price of 1147.20 is 55.1619, and, looking 2 columns to the right at a futures price of 1157.20, the net option delta is 56.0493.

Also, by using the '**Product**' drop-down box, you can filter for net delta by individual Product Series.

**Filtering Delta by Series**

When there are more than one Product Series in the portfolio for the chosen Combined Commodity, and the Product drop-down box is used to filter for a specific Product Series, the Opt.Delta row will display the net delta for that specific Product Series only.

*3) Net Delta*

Net Delta is the sum of Underlying and Option Delta.

*4) Gamma*

Gamma is the change in an option's delta (or portfolio of option deltas) for a one-unit change in the price of the underlying. This row displays the aggregate sum of the gammas for the combined commodity being analyzed.

*5) Vega*

Vega is the change in the value of an option or portfolio of options for a 1 percentage point increase in implied volatility.

*6) Theta*

Theta is the rate of decay in the time value of an option or portfolio of options . It is usually expressed as the change in the value of an option for one day’s passage of time.

*7) Rho*

Rho is the change in the value of an option for a 1 percentage point increase in interest rates.

**8) Risk**

The numbers in the risk row represent the theoretical gain or loss calculated using the incremented price of the underlying against the settlement price.

***Important note on Index-based and Yield-based implied volatility**

*For short-term interest rate contracts that are priced at 100 minus the yield, such as the CME's Eurodollar, Span RiskManager internally stores implied volatilities as 'Index-based' (based on the implied volatility of the underlying price), as opposed to 'Yield-based' (the implied volatility based on the yield derived from that price (100 minus the underlying price). For example, with Eurodollar futures at 98.04, a 98 call option may have a 'yield-based' implied volatility of 28% . The 'Index-based' implied volatility equating to 28% would be .0056. This is calculated as [implied vol * yield] / Index price. You can set Span RiskManager to display either yield-based or index-based vols for add-on type interest rate contracts in the Preferences section.*

**Using the Controls**

*Option Pricing Models*

The Option Pricing Model drop-down allows you to easily switch between one of 4 different option pricing models. To change models, simply choose a model from the list and click on 'Calculate Risk'.

*Main Variable*

The 'Main Variable' controls which sensitivity factor (Price, Time to Expiration, Volatility, Interest Rate, or Dividend Yield) will be analyzed and displayed horizontally across the exposure. Price is the factor that is most often used in these types of analyses but the other factors can be used as the Main Variable to pinpoint any kind of risk.

Figure 1.7 shows an example of the exposure using Implied Volatility as the Main Variable. It shows the Option Delta and risk of this portfolio recalculated down 2 vols, 4 vols, and 6 vols; and up 2,4,and 6 vols from the base volatility.

Using sensitivity factors other than Price as the Main Variable allows you to keep all other sensitivity factors constant and isolate changes in the greeks and risk for the given change in the Main Variable. You can do this analysis using any sensitivity factor as the Main Variable.

*Secondary Variable*

Use the Secondary Variable in conjunction with the main variable to gauge the effects of changes in price, implied volatility, time to expiration, interest rates or dividend yield with changes in the Main Variable. The Secondary Variable allows the user to gauge the effects of two variables changing at the same time. For example, Figure 1.8 shows the risk on a portfolio of S&P futures and options with the price of the underlying moving in increments of 5 points and implied volatility increasing and decreasing by 4 vols (in 2 increments).

You can use the scroll bar to see the effects of increases and decreases in implied volatility in conjunction with increases and decreases in the price of the underlying.

Below, in Figure 1.9, Time to Expiration is chosen as the Secondary Variable to show the effects on the portfolio of decreases in time to expiration (erosion). Figure 1.9 shows the effects of 2 days worth of erosion in conjunction with price moving in increments of 5 S&P points. This portfolio is net short option value (short vega) so, holding price and volatility constant, this portfolio gains $ as time passes. You can see the combined effects of price movement and passage of time as you look horizontally across the bottom rows of the exposure.

Figure 1.9

*Using Different Combinations of Main & Secondary Variables*

You can keep price movement constant and view the effects of changes in implied volatility in conjunction with changes in time to expiration by choosing implied volatility as the Main Variable and time to expiration as the Secondary Variable. Figure 1.10 shows implied volatility increasing and decreasing 1.5 vols in .5 vol increments in conjunction with the effects of 2 and 4 days reduced time to expiration (*row heights in the exposure can be re-sized or eliminated for convenience. In Figure 1.10, the bottom 2 rows have been eliminated for clarity*). This portfolio is net long Vega, therefore the portfolio loses value with a decrease in time to expiration.

__Display Graphics__

Click on the 'Risk Graph' button to view a graphical representation of the portfolio's risk.

__Exporting Data__

Risk Manager allows you to easily convert the data in the exposure to a .csv file for easy importing into other applications. Click on 'Export Data' and designate a file name and location from the dialogue box. Save the file. Open an application such as Excel or Access and open the saved file:

*Maintenance/Initial Margin:*

Span Risk Manager displays the total portfolio Maintenance and Initial margin.

To see the margin requirement for a particular combined commodity, exit the Analysis window and go the reports section in the main program. Click on the Requirements link.

A report will be generated like the one shown below:

Figure 1.11

**Position Details**

The position detail screen allows you to view all positions in the portfolio in one screen.

Figure 1.15

Figure 1.14

The Analyze Option window allows you to do several different types of analyses such as:

Pricing analysis

Price sensitivity analysis via the matrix

Discover how the option contributes to or reduces the overall risk of the portfolio

Fine tune the risk or hedge profile of the portfolio by finding the perfect option

Put/Call parity analysis

**A) Option Parameters**

You can change any or all of the fields in the Options Parameters section and recalculate values based on the changed parameters. Simply change any parameter, click the 'Calculate Value/Greeks' button and the values in the 'Calculations' section will be based on the new parameters you entered. Click on the 'Calculate Array' button in the Matrix Parameters section and both the Matrix and Graphics sections will reflect values based on the new parameters you entered in the Option Parameters section.

The 'Edit Prices' check box allows you to edit the underlying price and strike price in either 'contract value/strike value' format or the actual 'underlying price/strike price' itself. Also, use this button to toggle between editing either Option Price or Value in the Calculations section.

**B,C) Matrix & Matrix Parameters**

The Matrix functions and displays much like the Exposure in the Main Analysis window, the difference being that whereas the matrix in the Main Analysis window operates on an entire portfolio, the matrix in the Analyze Option window operates on the individual option.

The controls in the Matrix Parameters section determine how the matrix range and the intervals within that range will be displayed horizontally. The matrix is a powerful way to analyze the behavior and sensitivity of an option over a given set of variables. Also, you can change any of the pricing inputs in the Option Parameters section and/or the calculations section and see the results in the matrix by clicking on 'Calculate Array'.

**D) Calculations**

**CVM: **Change the Contract Value Multiplier to change the scale of the option (useful for Emini options).

**Price/Value:** Change the Price (Value) to calculate implied volatility and recalculate the greeks based on the new Price/Value. Also, the Matrix can be recalculated based on the new Price/Value by clicking on the 'Calculate Array' button in the Matrix Parameter section.

**Volatility:** Use this field to analyze the effects of changes in implied volatility.

**Pricing Model: **Choose among 4 different option pricing models for option valuation:

Black-Scholes

Merton

Adesi-Whaley

Cox-Ross-Rubinstein

**Exercise Style:** Choose between American or European.

Change any of the editable fields in this section to recalculate values based on the changed parameters. Click on 'Calculate Array' in the Matrix Parameters section to display the changed results in the Matrix. Click 'Calculate Volatility' to solve for volatility.

**E) Graphics:** Display the matrix values graphically.

**Notes**

If the *'Use dollar-denominated greeks' *option is turned on in the preferences section as shown in Figure 1.5, the quantities in this row display a dollar amount which is calculated as {quantity * contract value multiplier}. As an example, if a portfolio contains only 3 contracts in S&P 500 futures, the 'Underlying' row will show 750 (3*250).

*Tools>>Preferences>>Calculation Parameters*

Figure 1.5

***Important note on Underlying quantity and E-minis**: When E-minis are present in a portfolio, the quantity in the underlying row will not show fractional contracts. For example, if a portfolio contains a long position in 3 full-size S&P500 contracts and a short position in 1 E-mini S&P, the underlying row will show a quantity of long 2. It is recommended that when E-minis are present in a portfolio, you check the 'Use dollar-denominated greeks' checkbox in the preferences section. When this option is turned on, the quantity in the 'Underlying' row will be displayed as (quantity * contract value multiplier).

Using the previous example of +3 full-size S&P's and -1 E-Mini S&P, with the 'Dollar-denominated greeks' option turned on the underlying row would display: $700 calculated as: (3*250)-(1*50).

***Important note on delta and E-minis**:

When E-mini options are present in a portfolio, the quantity in the delta row does not distinguish fractional contracts unless 'Use Dollar-denominated greeks' is turned on in the Preferences section. As an example, assume a portfolio contains +10 March S&P 1045 puts with a .1487 delta and +10 March S&P E-mini 1045 puts also with a delta of .1487. Theoretically, both deltas are .1487, but the E-Mini contract is scaled 1/5th the size of the Big S&P contract. When not using the 'dollar-denominated greek' feature, the net delta for the above position would be -2.9745, which is simply the sum of the deltas of the full-size S&P options and the E-mini options, and would not be the proper hedge ratio. The solution to this is to check the 'Use dollar-denominated greeks' checkbox in the preferences section. With this option checked, the option delta is calculated using the contract value multiplier of the respective contract times the delta. In this case, the net delta would show as $446.17, calculated as:

(full-size S&P:) .1487*10***250** + (E-mini S&P:) .1487*10***50**

=371.75 + 74.35

= 446.10.

To arrive at the proper hedge ratio, simply divide by the contract value multiplier of the contract being used to hedge the position:

Full-size S&P contract value multiplier = 250

E-mini contract value multiplier= 50

446.17 / 250 = 1.78 big contracts or,

446.17 / 50 = 8.9 E-minis

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