Market indices

The S&P 500 is the measurement. The equity return is the risk factor: the change you apply to the stock sleeve. A Treasury yield is a measurement. The change in that yield is the interest-rate factor. A corporate spread is a measurement. The widening of that spread is the credit factor.

You do not have to own the index. Hundreds of separate stocks can still be represented by one equity factor. Beating the S&P 500 is a performance question. Revaluing the book when that index moves is a risk question. Both jobs use the name.

The model turns a published number into a balance-sheet question in this order: market data, risk factors, scenarios, asset and liability valuation, hedge valuation, then surplus.

An institutional scenario is a set of moves in these five, not a story about one ticker.

• Equity: the S&P 500 stands in for large U.S. companies. The Nasdaq-100 leans toward large technology companies. The Dow is a price-weighted list of 30 large companies. The Russell 2000 stands in for smaller companies.
• Rates: the Treasury curve, SOFR, and swap rates. A 2-year Treasury, a 10-year Treasury, and a 10-year swap rate can move by different amounts on the same day.
• Credit: an investment-grade corporate index and a high-yield index are different factors. A CDS index such as CDX is a spread proxy. It is not the bond itself.
• Volatility: VIX is a reading of implied volatility on S&P 500 options. MOVE is the cousin for Treasury-rate volatility. Neither one is the volatility of one option in the book.
• Inflation: CPI is a price index. Breakeven inflation is the market’s priced expectation, read from nominal bonds against inflation-linked bonds. It is not a print of next year’s CPI.

Oil, natural gas, and gold are further factors if the book holds them. They are not a sixth pillar on this page.

The first table names the measurement. The second names what that measurement is allowed to reprice.

This sleeve is labeled as its own classroom, separate from the shock lab. It is $200 million of equity with a beta of 0.80 to the S&P 500. The index falls 20%. The sleeve does not have to fall 20%.

Portfolio move ≈ beta × index move = 0.80 × −20% = −16%. Dollars: $200 million × −16% = −$32 million. If the beta were 1.0, the same index fall would be −$40 million. The beta is why “the S&P 500 fell 20%” is not yet the balance-sheet number.

The shock lab’s equity sleeve is the smaller book: $20 million that moves one-for-one with the slider. That is the beta-1 case. A −20% slider is −$4 million there, not −$32 million.

One equity factor is still a shortcut. A classroom stress can split the sleeves: large-cap −20%, small-cap −28%, international −24%, and emerging markets −32%. Growth and value can be their own factors. The engine applies each shock to the sleeve that owns it.

One yield is one point. The curve is several factors. Saying “rates are 4%” hides a steepener. The yield curve page draws the shapes. The picture here is a move that is not parallel: from a flat 4%, the 2-year rises 50 basis points, the 5-year rises 75, the 10-year rises 100, and the 30-year rises 80.

That curve is a classroom picture, not today’s Treasury curve. A scenario that says the 10-year goes from 4.40% to 5.40% is a +100 basis point factor. The same day can reprice bonds, the liability discount, reinvestment, policyholder behavior, swaps, swaptions, and embedded options.

Read both sides before you stop. The duration-page book is assets of $100 million at duration 6 and liabilities of $100 million at duration 12. Up 100 basis points in parallel is about −$6 million on the assets and −$12 million on the liabilities. Surplus rises about $6 million before any hedge, because the promise got cheaper by more than the bonds. An asset-only loss of $6 million is the wrong ALM total.

The named shapes — parallel, steepener, flattener, twist — are the market shocks lab.

A credit spread is the extra yield over a Treasury of a similar maturity. A corporate bond at 5.50% against a Treasury at 4.00% has a spread of 1.50 percentage points, which is 150 basis points. That extra yield is what the market asks for credit and for the other differences from the Treasury. It is not a forecast that the issuer will default.

On the shock-lab bonds, $80 million with a spread duration of 5, a 150 basis point widening is −$80 million × 5 × 0.015 = −$6 million. The lab’s starting slider is +50 basis points, which is −$2 million on those same bonds. Investment-grade spreads and high-yield spreads are different factors. A widening can mark the corporate bond down even when the Treasury yield did not change.

VIX at 15 is a calm classroom reading of equity-option volatility. VIX at 35 is a stress reading. MOVE is the same kind of reading for Treasury volatility. The width can jump before the underlying has moved far. That is why “rates went up” is not a complete scenario for a swaption, a cap, a mortgage, or a guarantee.

Who owns the option decides the sign. A payer the book owns can gain when rate volatility rises. A guarantee the book has written can become a more expensive liability, because the option the customer holds is worth more. The teaching size is the shock lab’s $150,000 per volatility point. Ten points is $1.5 million. The volatility lesson defines the width. Swaption volatility is where the rate grid lives. The sketch here is the idea of that grid: a calm reading of 70 basis points against a stress reading of 120, with expiry and strike as the two axes.

CPI is the price index. Take a $10 million expense. At 3% inflation it is $10 million × 1.03 = $10.3 million. At 6% it is $10 million × 1.06 = $10.6 million. The difference is $300,000. The same 3 percentage points on a larger inflation-linked promise is the same percent of that promise.

Breakevens are what the bond market has priced for inflation, not a print of the next CPI release. Higher inflation can be followed by a higher policy rate, higher market yields, lower bond prices, and a change in the rate used to discount liabilities. Those steps are a possible path. They are not one-for-one, and they are not a forecast.

The five pillars do not have to move alone. A stress mix can be equities down, credit spreads wider, and volatility up, while Treasury yields fall. An inflation mix can be CPI up and yields up, with bond prices down. The correlation lesson is why a calm link can tighten in that stress. The menu below is the stress sheet. It is not a second valuation of the classroom book. The shock lab is where a labeled book is turned into dollars.

Historical stress replays a past mix. Hypothetical stress is a mix you write down. Both are on the stress testing page.

A retail question stops at the asset line: how much did the bonds lose? The ALM question is what happened to assets, liabilities, and the hedge together.

The shock lab starts at +100 basis points of yield, +50 basis points of credit spread, −20% equity, and +10 volatility points. On that labeled book the surplus change is +$6.7 million, because the longer liabilities are marked down by more than the bonds, and the hedge coefficient gains when yield and volatility rise. Walk those lines in the shock and net impact lab. This page does not add a second portfolio.

Read down the left column, then the right. A rate rise can keep going: bond values, liability value, reinvestment, policyholder behavior, swaps, collateral, and only then surplus.