✦ ✦ ✦
Some finance professionals promote B&H (buy & hold, value or market variety) as a 'disciplined' approach that has performed well over the 'long term'. Unfortunately, too many seek to abstract their own experience from reality. They fail to realize that their own experience (even if 10/20/30 years in the making) is nothing more than one example of what is realistic. Basing claims on the quality of one's research is preferable to the quantity of one's experience (though the simple act of storytelling makes the latter much easier). For the uninitiated, quality research in the field of finance requires quality mathematics.
Low Interest Rates
Interest rates are currently at cycle lows. Given the length of these cycles, the upcoming increasing rate trend will constitute a
]]>This article is an excerpt from the new book The Value in Volatility by Alpay Kaya. It is reprinted with permission.
✦ ✦ ✦
Some finance professionals promote B&H (buy & hold, value or market variety) as a 'disciplined' approach that has performed well over the 'long term'. Unfortunately, too many seek to abstract their own experience from reality. They fail to realize that their own experience (even if 10/20/30 years in the making) is nothing more than one example of what is realistic. Basing claims on the quality of one's research is preferable to the quantity of one's experience (though the simple act of storytelling makes the latter much easier). For the uninitiated, quality research in the field of finance requires quality mathematics.
Low Interest Rates
Interest rates are currently at cycle lows. Given the length of these cycles, the upcoming increasing rate trend will constitute a
The author offers a few examples over a 2-year timeframe. As he did not specify dates or number of trading days (and his numbers seem to coincide with non-adjusted prices) the numbers shown below are my own calculations. As for the definition of the ideal LETF referenced in the tables, it assumes zero financing costs, zero management fee, zero transaction costs, and perfect tracking.
False
]]>Just as markets are positioned at the crossroads of mathematics and human behavior, they serve as a showcase of the interplay between objectivity and subjectivity. One popular way people display their flippant attitude towards objectivity is by proclaiming causal relationships without any accompanying verification (or any attempt at such). I am referring to a Wall Street Journal MarketWatch commentary (from The Trading Deck, 29 Nov. 2012) in which Leveraged ETF (LETF) decay is incorrectly attributed to 2 sources: liquidity risk and rollover risk.
The author offers a few examples over a 2-year timeframe. As he did not specify dates or number of trading days (and his numbers seem to coincide with non-adjusted prices) the numbers shown below are my own calculations. As for the definition of the ideal LETF referenced in the tables, it assumes zero financing costs, zero management fee, zero transaction costs, and perfect tracking.
False
Example: Consider a 2-day example summarized below, where r_{i} is the continuously calculated (log) return and a_{i} is the percent change.
r_{1} | a_{1} | r_{2} | a_{2} | |
---|---|---|---|---|
+1x ETF | +4 % | +4.08 % | -4 % | -3.92 % |
-1x ETF | -4.17 % | -4.08 % | +3.85 % | +3.92 % |
Leverage | -1.04 | -1 | -0.96 | -1 |
The 'logical flow' for each day is a clockwise circle: r_{i}(index) = r_{i}(+1x) → a_{i}(+1x) → a_{i}(-1x) → r_{i}
]]>It may be easy to react by saying "no" since +1 and -1 are the same magnitude, meaning the percent change of the -1x fund is equal and opposite to that of the +1x fund. On the other hand, investors have noticed that inverse funds seem to exhibit negative drift consistent with leveraged ETFs. Obviously, something is different and worthy of considered analysis.
Example: Consider a 2-day example summarized below, where r_{i} is the continuously calculated (log) return and a_{i} is the percent change.
r_{1} | a_{1} | r_{2} | a_{2} | |
---|---|---|---|---|
+1x ETF | +4 % | +4.08 % | -4 % | -3.92 % |
-1x ETF | -4.17 % | -4.08 % | +3.85 % | +3.92 % |
Leverage | -1.04 | -1 | -0.96 | -1 |
The 'logical flow' for each day is a clockwise circle: r_{i}(index) = r_{i}(+1x) → a_{i}(+1x) → a_{i}(-1x) → r_{i}
Recently I came upon a finance blog posting declaring that LETFs do not suffer from this insidious loss of value. The author assumes the future expected value of an index equals its current value, and under this assumption, the future expected value of a leveraged ETF tracking that index equals its current value. The conclusion is correct; unfortunately, laypeople will be misled by it.
Although the assumption effects a loss of generality, it is not the issue. The author's conclusion is consistent
]]>Since shortly after leveraged ETFs appeared in 2006, the investing public has, on and off, discussed a phenomenon termed "negative drift" or "decay". Typically described by example in flat markets, it refers to a loss in LETF value over a period the tracked index (and 1x-leveraged "standard" ETF) is flat. This is actually just an example of negative drift but serves the purpose of a working definition.
Recently I came upon a finance blog posting declaring that LETFs do not suffer from this insidious loss of value. The author assumes the future expected value of an index equals its current value, and under this assumption, the future expected value of a leveraged ETF tracking that index equals its current value. The conclusion is correct; unfortunately, laypeople will be misled by it.
Although the assumption effects a loss of generality, it is not the issue. The author's conclusion is consistent