by Charles Cheng, CFA & MBA

 

 

We are often told that to get high returns, you must take high risks. This is not always true. Many like to chase volatile investments that promise explosive year-over-year gains. However, the mathematics of long-term compounding tells a different, more nuanced story. A volatile portfolio that experiences severe drops, or drawdowns, can end up with less money than a “boring,” stable portfolio, even if its average annual return is higher.

我們常說，要獲得高回報，就必須承擔高風險。　這並非總是正確的。　許多人喜歡追逐那些有望實現年度爆炸式增長的波動性投資。　然而，長期複利的數學原理卻講述了一個截然不同、更微妙的故事。　一個波動性較大的投資組合，如果經歷大幅下跌或回撤，最終的收益可能比一個「平淡無奇」的穩定投資組合更少，即使其年平均回報率更高。　

 

There is a difference between two types of investment averages. The first is the Arithmetic Mean, or the “simple” average. This is what most people think of: you add up the returns for each year and divide by the number of years. It’s simple, but it’s misleading because it ignores the effect of compounding. The second, and more important, is the Geometric Mean, or the “real” average. This is what you experience in your account. It’s the compound annual growth rate (CAGR) that measures how your money grew over time, accounting for the ups and downs. When returns are volatile, the simple average will always be higher than the real average you earn. The gap between them is a mathematical penalty known as “volatility drag.”

投資平均值有兩種。　第一種是「算術平均數」（Arithmetic Mean），也就是「簡單」平均值。　這是大多數人所想到的：將每年的報酬率相加，然後除以年數。　這很簡單，但具有誤導性，因為它忽略了複利的效果。　第二種，也是更重要的，是「幾何平均數」（Geometric Mean），或稱「真實」平均值。　這是您帳戶中實際體驗到的。　它是「年複合增長率」（CAGR），衡量您的資金隨時間增長的真實情況，並已考慮到漲跌波動。　當報酬率不穩定時，簡單平均值（算術平均）將永遠高於您賺到的真實平均值（幾何平均）。　兩者之間的差距是一種數學上的懲罰，稱為「波動性拖累」（volatility drag）。　

 

Let’s compare two portfolios over 10 years, both starting with $10,000. Portfolio A is stable, earning 6% every single year. Portfolio B is volatile, with returns like +30%, -15%, +20%, -10%, and so on. Over the 10 years, Portfolio B’s simple average return is 6.5%, which looks better than Portfolio A’s 6.0%. However, at the end date, the stable Portfolio A has grown to $17,908, while the volatile Portfolio B is worth only $17,506. Even though Portfolio B had a higher simple average, its volatility created a “drag” that eroded the returns. The stable, “boring” Portfolio A won in the long run.

讓我們來比較一下兩個10年期的投資組合，起始資金都是10,000美元。　投資組合A較穩定，每年收益率為6%。　投資組合B波動較大，收益率分別為+30%、-15%、+20%、-10%等等。　 10年間，投資組合B的簡單平均報酬率為6.5%，看起來比投資組合A的6.0%好。　然而，截至年底，穩定的投資組合A已成長至17,908美元，而波動較大的投資組合B的價值僅為17,506美元。　儘管投資組合B的簡單平均收益率更高，但其波動性造成了“拖累”，侵蝕了收益率。　從長遠來看，穩定且「乏味」的投資組合A最終勝出。　

 

A drawdown, which is the decline from a portfolio’s peak to its trough, is a major reason for this. The math of recovering from a loss is unforgiving and works against you. For instance, if you lose 10%, you need an 11% gain to get back to even. If you lose 25%, you need a 33% gain. And if you lose 50%, as many did in the 2008 crisis, you need a 100% gain just to get back to where you started. Every time your portfolio suffers a large drawdown, you are working from a smaller capital base. This means the same percentage gain on your remaining money earns you fewer dollars than you lost on the way down. This process of having to “climb out of a hole” is a major destroyer of long-term compounding. A stable portfolio that avoids deep losses doesn’t have to waste time and energy just getting back to even.

回撤(drawdown)，即投資組合從高峰跌至谷底的過程，是造成這種情況的主要原因。　從損失中恢復的計算過程是惡劣且對你不利的。　例如，如果你虧損10%，你需要11%的收益才能回到平衡。　如果你虧損25%，你需要33%的收益。　如果你虧損50%，就像2008年金融危機中的許多人一樣，你需要100%的收益才能回到起點。　每次你的投資組合遭遇大幅回檔時，你的資本基礎都會減少。　這意味著，你剩餘資金的相同百分比收益，給你帶來的收益比你在下跌過程中損失的要少。　這種「爬出深淵」的過程是長期複利的一大破壞者。　一個能夠避免巨額虧損的穩定投資組合，無需浪費時間和精力來恢復平衡。　

 

Beyond the mathematics of compounding, there could be other costs to taking drawdowns, including negative psychological effects on the investor as well as unwarranted changes in portfolio strategy. These can cause investors to sell out of fear and wait too long to come back into the market, leading to large opportunity costs or even permanent losses that they can’t recover from if the loss is too big.

除了複利的數學計算之外，承擔回撤還可能帶來其他成本，包括對投資者的負面心理影響以及投資組合策略的不必要的調整。　這些因素可能導致投資者出於恐懼而拋售，並等待太久才重返市場，導致巨大的機會成本，甚至造成永久性損失，如果損失過大，它們將無法被挽回。　

 

It’s important to keep in mind the possible range of returns you could have over the course of your entire investment horizon, not just the ideal outcome. This is especially important when nearing retirement. If you are withdrawing money and the market crashes, you are forced to sell your investments when they are cheap. This can drain your account very quickly. A stable portfolio can protect you from having to sell at the worst possible time. A key lesson is that you can often win by not losing. Avoiding the big drops is a great way to grow one’s wealth.

重要的是要記住你在整個投資期間內可能獲得的回報範圍，而不僅僅是一個理想的結果。　這一點在接近退休時尤為重要。　如果您正需要提取資金，而此時市場崩盤，你就會被迫在價格低廉時拋售你的投資。　這會很快耗盡你的帳戶資金。　穩定的投資組合可以保護你免於在最糟糕的時機拋售。　一個重要的教訓是，你往往可以透過不虧損來獲利。　避免大幅下跌是增值財富的絕佳途徑。　

 

 

This article reflects the personal views of the author and not any firm’s and should not be viewed as an investment recommendation.

 

 

 

 

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