The key distinction is between owning a mortgage-related security and making a derivative contract whose payoff depends on that security.
Suppose there is $100 million of mortgage bonds. Investors can actually own those bonds and receive payments generated by the underlying mortgages. If enough homeowners default, those bonds can suffer losses.
But financial institutions also created credit default swaps (CDS) referencing mortgage bonds and CDOs. A CDS works somewhat like insurance: one party periodically pays a premium, while the other promises to make a payment if the referenced security suffers specified credit losses.
Importantly, you did not necessarily have to own the underlying mortgages to enter into such a contract. This allowed multiple parties to make separate bets based on the performance of the same pool of mortgage debt.
A synthetic CDO took portfolios of these credit exposures and divided their risks into tranches. Instead of primarily owning actual mortgages or mortgage bonds, a synthetic CDO could obtain exposure through CDS contracts referencing mortgage securities.
This is where the magnification came from. Imagine $100 million of actual mortgage securities exists, but several different derivative contracts each reference those same securities. The economy has not created several additional sets of houses or mortgages—it has created several additional financial claims whose values depend on the original mortgages.
When mortgage defaults increased, losses therefore did not stop with the institutions directly holding mortgage-backed securities. They also affected CDO investors, CDS sellers, synthetic CDOs, banks, insurers, and other counterparties that had written contracts tied to those securities.
There was another problem: leverage. Many financial institutions financed investments with substantial borrowed money. A relatively small percentage loss in asset value could therefore eliminate a much larger percentage of an institution's equity.
It is also important to distinguish notional value from actual losses. Saying that derivatives were some multiple of the underlying mortgage market does not mean that every $1 of mortgage losses automatically created $20 of economic losses. The notional amount measures the value referenced by derivative contracts, not necessarily the amount that will ultimately change hands.
Finally, not every derivative became worthless. The crisis involved falling mortgage-security values, CDS obligations, leverage, uncertainty about counterparties, and severe liquidity problems. Because institutions did not always know who was exposed to whom—or whether counterparties could honor their obligations—credit markets began to freeze.
So the "atomic bomb" analogy in The Big Short is essentially describing how derivatives allowed the financial system to create many additional layers of exposure to the same underlying mortgage risk. When the mortgages deteriorated, those interconnected and leveraged claims transmitted and amplified the losses throughout the financial system.
