Geometric Linking

Geometric Linking (also known as the Time-Weighted Rate of Return or TWRR) is a standard method for calculating an investment portfolio's performance. Its magic lies in what it ignores: the distorting effects of cash flowing into or out of the account. Imagine you invest $1,000, and a month later, you add another $100,000 right before the market soars. A simple return calculation would look incredible, but was it your investing genius or just lucky timing with your deposit? Geometric linking answers this question by isolating the performance of the investments themselves, providing a true measure of the underlying strategy or the skill of the portfolio manager. It does this by breaking the total time into smaller periods based on when cash flows occur, calculating the return for each period, and then “linking” them together geometrically (i.e., by multiplying them). This makes it the gold-standard method used by the investment industry to compare the performance of different funds and managers against a benchmark, ensuring an apples-to-apples comparison.

Think of your portfolio as a soup being cooked by a chef (your investment strategy). If you, the investor, keep throwing in new ingredients (cash deposits) or scooping some out (withdrawals), it becomes impossible to judge the quality of the chef's original recipe. Did the soup get better because of the chef's skill or because you added a delicious truffle at the last minute? Geometric linking solves this problem. It effectively “tastes” the soup's performance in between each of your additions or removals. By doing so, it strips away the impact of your cash flow timing and tells you exactly how well the chef's recipe—your investment strategy—is actually performing on its own. It answers the crucial question: “How well did my chosen investments perform?” This is a fundamentally different question from “How well did my money do?” For evaluating a strategy or a professional manager, the first question is the only one that matters.

Let's say you're a diligent saver and want to track how well your stock-picking skills are doing, independent of when you get paid and can add more funds.

The first step is to slice your total investment period into smaller “sub-periods.” A new sub-period begins every time cash is added or removed.

You then calculate the simple return for each of these clean sub-periods.

• Period 1: You start the year with a $10,000 portfolio. After six months, it has grown to $11,000. You haven't added or removed any money.
  • Return for Period 1 = ($11,000 / $10,000) - 1 = 0.10 or 10%
• Period 2: Right after that, you deposit another $5,000. Your new starting balance for this period is $11,000 + $5,000 = $16,000. Unfortunately, the market takes a tumble, and by the end of the year, your portfolio is worth $14,400.
  • Return for Period 2 = ($14,400 / $16,000) - 1 = -0.10 or -10%

Now, you “geometrically link” these sub-period returns. You don't just add them up (10% - 10% = 0%). Instead, you chain them together through multiplication to find the true compounded return of the strategy. The formula is: [(1 + Return of Period 1) x (1 + Return of Period 2)] - 1

• Plugging in our numbers: `[(1 + 0.10) x (1 - 0.10)] - 1`
• This becomes: `[1.10 x 0.90] - 1`
• Which equals: `0.99 - 1 = -0.01` or -1%

Your investment strategy actually had a negative return of 1%. The simple “paper” return might look better (you started with $10,000 and ended with $14,400, not counting the $5,000 you added), but geometric linking gives you the unvarnished truth about your strategy's performance.

The main alternative to geometric linking is the Money-Weighted Rate of Return (MWRR), which you might also know as the Internal Rate of Return (IRR). The difference is simple but profound:

• Geometric Linking (TWRR): Measures the performance of the strategy. It ignores the effect of your cash flow timing. This is the manager's return. It's best for comparing your strategy against the S&P 500 or another manager.
• Money-Weighted (MWRR): Measures the performance of your capital. It is heavily influenced by the timing and size of your cash flows. This is your personal return. It's best for answering, “What return did I actually make on the dollars I invested?”

In our example above, your MWRR would be positive because a smaller amount of capital was exposed to the 10% gain, and a larger amount was exposed to the -10% loss. The TWRR, however, correctly shows that the strategy itself was down 1%.

For a value investor, this distinction is not just academic; it's a critical tool for self-assessment and discipline. The core of value investing is patiently buying wonderful companies at fair prices, based on rigorous analysis of their intrinsic value. Your success should be measured by the quality of that analysis, not by whether you got lucky and received a bonus to invest just before the market rallied. Geometric linking provides this honest feedback. It helps you answer questions like:

• Is my method for picking undervalued stocks actually working over time?
• Am I outperforming my chosen benchmark because of skill or just lucky cash-flow timing?

By focusing on the geometric or time-weighted return, you keep your attention on the quality of your investment decisions. This fosters the patience and analytical rigor necessary to be a successful long-term investor, preventing you from being fooled by randomness or mistaking a lucky deposit for investing genius.