How do I get these numbers?

The idea behind this is that venture capital is currently a very attractive investment since risk-free yields (and thus all yields) on financial assets are very low. As the risk-free rate rises, risky venture capital will become a less attractive investment, and startups will have trouble raising money. They will then fail, and the bad publicity will hurt perceptions of startups, causing more money to leave the venture capital sector and more startup failures. Of course, the tech bubble might pop for various other reasons.

In the true spirit of financial analysis, I make many simplifying assumptions of questionable validity to obtain a single number to predict a very complex event many years into the future.

I assume that venture capital is invested for 7 years on average and that the desired yearly return is 8%.

I compare the future 7-year risk-free rate of return to the 8% desired return. The higher the risk-free rate, the higher the probability of the startup bubble popping.

How I get future interest rates

It's possible to calculate future interest rates from current interest rate data. The future interest rate is called the forward rate. I calculate it based off of the zero-coupon treasury yields. I use zero-coupon treasuries because they do not pay a coupon, so I don't need to worry about what rate the coupon payment will be reinvested at. The future rate is calculated assuming that no arbitrage exists - that is, if the rate were anything else, market participants could make trades that would guarantee them a risk-free profit. This becomes less accurate for predictions further into the future.

Problems with my approach

Inflation

The yields are not adjusted for inflation. I need to compare the yields of coupon-bearing treasuries with the yields of coupon-bearing inflation-adjusted treasuries to get the market's future inflation expectations, and then adjust the zero-coupon yields accordingly. This would have been too much work to do from the beginning, but I will do it eventually.

Probability function

Obviously the probability function is completely baseless. It’s there just to normalize the forward rate curve. Obviously the amount of money invested in web startups depends on more than just the risk-free interest rate, such as market perception, previous returns, attractiveness of available investments, inflation expectations, etc.

Calculating a single probability number for something as complex as the amount of venture capital invested in the future is probably impossible. In order to get a true idea of the probability of the bubble popping, you need to look at all of the data and use your judgement to make an educated estimate.

For the curious, the probability function is simply a double logistic function with scale factor of 5.

Questionable data

I get the zero-coupon treasury data from the wall street journal. The yields for the longer-dated bonds don’t seem to be calculated correctly, and the prices seem to show arbitrage opportunities for some maturities.

Predictions of rates far into the future

The farther into the future predictions go, the less valid they become. Predicting anything far into the future is very error-prone. These predictions show the arbitrage-free predictions of the market, but executing arbitrage becomes much less attractive when the profits will only be realized far in the future. Therefore, the predictions of rates far into the future are pretty much completely invalid.