【Asset Allocation】Gain-Loss Asymmetry

Gain-Loss Asymmetry

Simple arithematic poses two consecutive days with 50% gain and 50% loss, respectively to even out. However, investing runs on a compounding basis. This simple but crucial aspect more often than not exposes investors to so-called "Gain-Loss Asymmetry". This is to say, the percentage gain required to even out the loss is much larger than the percent lost."

Proposition 1
Investment runs on a Compounding (Geometric) Basis 

 

Let's continue with the example set forth in the opening.

 

Q1. Assume your APPLE share soar by 50% on the first day, but dropped by 50% the next day. How much would you gain or lose?

 

The answer is 25% loss (not 0), because:

Day 0: 100%

Day 1: 150% (1 x 1.5)

Day 2: 75% (1.5 x 0.5)

 

Q2. Assume your APPLE share soar by 10% for the next 10 consecutive days. How much would you gain or lose?

 

The answer is 159% gain (not 100), because:

Day 0: 100%

Day 1: 110% (1 x 1.1)

Day 2: 121% (1.1 x 1.1) 

...

Day 10: 259%

 

Q3. Assume your APPLE share suffered 50% loss for two consecutive days. How much would you lose?

The answer is 75% loss (not 0), because:

Day 0: 100%

Day 1: 50% (1 x 0.5)

Day 2: 25% (0.5 x 0.5)

 

 

The three questions illustrate that:

1. When same % of gain and loss are repeated, you tend to lose.

2. When frequently gains, the magnitude of growth exponentialially increases.

3. When frequently loses, the magnitude of loss exponentially diminishes.

 

 

Proposition 2
Gain-Loss Asymmetry

Q1. Assume your APPLE share tanked by 50%. How much should you earn in % to recover from the loss?

The answer is 100% (not 50%), because:

 

Day 0: 100%Day 1: 50% (1 x 0.5)Day 2: 100% (0.5 x 2)

 

This example illustrates that the % of gain required to recover a certain % of loss is much larger. 

 

Proposition 3
Cost of Volatility

Here, volatility is dispersion of return or simply the magnitude of percent change.

 

Let's assume:

1. APPLE gained 50% then dropped 50%

2. BANANA gained 20% then dropped 20%

3. CHERRY gained 10% then dropped 10%

Q1. Which company has the best return (gain)?

The answer is CHERRY, because:

 

1. APPLE: 100 x 1.5 x 0.5 = 0.75 (75%, 25% loss)

2. BANANA: 100 x 1.2 x 0.8 = 0.96 (96%, 4% loss)

3. CHERRY: 100 x 1.1 x 0.9 = 0.99 (99%, 1% loss)

 

Eventhough same level of gain and loss occurred, less the magnitude of percent change higher the gain (lower the loss). To generalize, high volatility tends to lower return, whereas low volatility tends to higher return.

 

Takeaway

These questions point to the:

 

1. Need to maintain the % loss lower than % gain (compounding basis)

2. Need to minimize the frequency of loss events (gain-loss asymmetry)

3. Need to reduce the volatility of gain and loss (cost of volatility)

 

Based on these fundamental characteristic of investing or money, per se, the most important goal changes from "maximizing return" to "minimizing loss". On that note, the entire series on porfolio management and asset allocation will focus on how to "minimize loss".