by YOLOQuant

I’ve seen a lot of misunderstanding across about the effect of rates on equities, so I figure I’d hop off of WSB to give an explainer about the relationship between stocks and interest rates, and show why the current sell off makes sense.

**Where do interest rates come from?**

Money has time value. Money today is usually worth more today than money tomorrow. How do we measure the time value of money? Interest! When we loan money out, we demand a return. What goes into an interest rate? There are 3 primary factors:

- *What do I think inflation is going to be?*Say you estimate inflation to be 3% and rising, you’ll demand a far higher interest rate to protect yourself.
- *How risky is this loan?*Your lend to a group of risky businesses, you might jack up interest rates to make sure if one goes under, you’ll make your money back from the rest
- *How much is everyone else willing to lend for?*You’ll need to compete with other lenders which helps determine the final interest rate.

**US Treasuries: King of Bonds**

So US government debt is considered primo with near 0 risk of default. The rates on US government debt determines whats known as the *risk free rate*.

The US issues debt at several different maturities from weeks, to months, to years. If we line up these interest rates, we get what is known as the yield curve.

To reiterate, these rates are determined by the market and are manipulated by the Federal Reserve, which attempts to intervene in the market to get rates to its targets. When the Fed comes out and says it wants rates to stay near zero, this one of the ways they do it.

And this is exactly what happened during the corona crash, interest rates went to zero across the curve.

**How to Value a Company**

Let’s say we have two companies. $BRR and $GRO. Let’s say we’re certain of their future cash flows.

- BRR is runs a money printer and makes $10M a year.
- GRO is a growth stock that’s expected to make $100M a year in a decade.

How do we value these two companies based on cash flow alone? For simplicity, let’s only look at the first 10 years. We need to determine the present value of the money the company makes in the future.

What is money from n years from now worth today? money / (1 + risk_free_rate)^n. So we can represent todays value for 10 years of cash flow like this:

Value = ($$$ Year 1) / (1 + r) + … + ($$$ Year 10) / (1 + r)^10

This is one of the ways to come to an intrinsic valuation of a company.

**How Rates Affect Value**

So which company do you think is worth more? BRR or GRO.

Well that depends on the interest rate! Let’s say interest rates are at 0 or near zero. Their valuations taking no other factors into account are nearly the same: $100M.

Now let’s start cranking up the interest rate slowly to see what the current valuation is.

r | BRR | GRO |
---|---|---|

0.0% | 100M | 100M |

0.5% | 97M | 95M |

1.0% | 94M | 90M |

2.0% | 90M | 82M |

4.0% | 81M | 67M |

*As interest rates go up, the company that depends more on future earnings (GRO) is getting whacked. A move 0% to 2% knocks off almost 20% in one shot.*

*SPECIAL NOTE: The risk free rate is actually extremely low right now, around 0.05% due to Fed intervention. With the move in the 5 and 10 year, the market is likely anticipating an acceleration much sooner than expected.*

**So why the fuss all of a sudden?**

Stocks went flying higher under the assumption that the fed would remain dovish, work to keep interest rates low, and would not be able to produce inflation over 2% if it wanted to. For a lot of reasons, people were betting that if that inflation would appear any were it would happen farther out in time near the 30Y. Given they figured the 5Y would stay low, and the 30Y would go high they shorted the 30Y bonds and went long 5Y. However, 5Y and 10Y treasury yields suddenly spiked making everyone ask whether inflation would come sooner and faster. People hoped the fed wold say something to alleviate this, but instead Powell had stated in September that he’s fine with inflation running hot over 2% (which no one seems to have believed) , and the fed today reiterated its not going to do anything about it in the short run. Hence, yields are still rising and equities are continuing to fall. Add to this all the froth and speculation, a 20-30% correction makes a lot of sense in overheated names.

**Caveats about the analysis above**

- The interest rates are made up. In reality, the risk free rate is a lot lower. The true risk free rate, for example, is typically associated with 3 month bills ~0.05%, at 10 years that yields (1.005)^10 = 1.05%.
- Equity risk premium is also another factor.
- BRR is actually a better play since the risk free rate for earlier years will likely be lower than those farther out in time.
- You shouldn’t stop counting after year 10. You in theory can go out to infinity, and if rates are near zero, valuations for a growth company blow up too.
- In most discount cashflow analysis, you don’t use the risk free rate instead you use a discount rate specific to the company that takes risk into account for that company. In this case, it’s fine to use the risk free rate since we assume we somehow know exactly how much the company will make (certainty equivalent). In the real world, we predict future cash flows by licking a finger sticking it in the air, and guessing which way the wind will blow.

**Inflation! Waddabout gold?**

If treasury yields stay above inflation, gold prices fall. That’s because it’s better to own a sheet of paper with a yield than a rock. Gold will only benefit if the Fed works to suppress rates farther out on the curve. This is why the price of gold is negatively correlated with real interest rates*.*

Disclaimer: This information is only for educational purposes. Do not make any investment decisions based on the information in this article. Do you own due diligence or consult your financial professional before making any investment decision.