Stock vs Bonds

📌 Why Long-Term Stock Guarantees Are More Expensive Than They Look

I recently came across a fascinating “Business Snapshot” in John Hull’s classic textbook Options, Futures, and Other Derivatives. It deals with a question many investors assume has an obvious answer:

“If you invest for the long run, aren’t stocks guaranteed to outperform bonds?”

Hull shows that this intuition breaks down the moment you turn it into an actual guarantee.
If a fund manager promises that stocks WILL beat bonds in exactly 10 years, that commitment is mathematically equivalent to giving investors a long-dated put option on the index. And long-dated downside protection—especially on volatile markets—is surprisingly expensive.

Business Snapshot 16.1 — Can We Guarantee That Stocks Will Beat Bonds in the Long Run?

---

🔍 What Hull Demonstrates

It is often said that long-term investors should choose stocks over bonds.
Imagine a U.S. fund manager running an S&P 500 index fund who wants to guarantee that the fund will outperform risk-free bonds over the next 10 years.

Historically, this sounds like an easy promise: stocks have outperformed bonds in almost every 10-year period.
But financially, this guarantee is far from cheap.

Hull assumes:

• Index today: 1,000
• Dividend yield: 1%
• Volatility: 15%
• 10-year risk-free rate: 5%

To beat bonds, total stock return must exceed 5% annually.
With dividends contributing 1%, capital gains must supply the remaining 4%.

This means the index must reach approximately 1,492 in 10 years.

Guaranteeing bond outperformance is therefore equivalent to giving investors a 10-year European put option with strike 1,492.
Using standard valuation, Hull shows the put is worth 169.7, meaning:

👉 The guarantee costs 17% of the fund

—far too valuable to give away for free.

---

💡 My Additional Insight: The Power of a Performance Window

After studying Hull’s example, I explored a natural extension:

What if the guarantee isn’t tied to a single point in time (exactly year 10), but instead allows the market more time to outperform—say, any time during years 10 to 12?

A 2-year performance window dramatically reduces the probability that the guarantee triggers.
Markets often recover from temporary drawdowns if given time, and the fund manager’s downside risk shrinks.

As a result, the cost of the guarantee drops substantially — down toward roughly 5% rather than 17%.

Adapted from:

Options, Futures & Other Derivatives, John C. Hull