We introduce the notion of a patience premium, which is based on the concept of ambiguity aversion and is an ambiguity premium. We identify three reasons for the existence of the patience premium: Certainty preferences: perceived confidence in the expected performance; Comparison with peers:...

VaR_Delta-Normal is derived from a Put option, named PVaR_Delta-Normal and Expected_Shortfall, PSF_Delta-Normal – the latter a coherent measure – guaranteeing VaR can never be larger than the fund value. Current standard VaR_Delta-Normal uses covariances calculated from the entire...

We present comprehensive evidence in support of giving liquidity equal standing to size, value/growth, and momentum as investment styles, as defined by Sharpe (1992). First, we show that financial market liquidity, as identified by stock turnover, is an economically significant indicator of...

These days it's become convention (reinforced by the media's treatment of wealth) to assess our net worth by tallying up the market value of our financial assets, even though it's more natural and useful to think of our wealth as a stream of dollars over time given the nature of our income and...

In understanding how leveraged ETFs perform, we'll uncover an important lesson relevant to all investing: how your choice of investment size can be more important than your choice of investment. To summarize, highly leveraged long and short ETFs provide a perfect illustration of how...

There has been considerable research into dynamic global tactical asset allocation (GTAA) strategies driven by simple measures of Valuation and Momentum applied to a baseline balanced portfolio of equities and fixed income (see Blitz and van Vliet 2008, Wang and Kochard 2011, Gnedenko and Yelnik...

The longest bull market in US stock market history is over. Uncertainty over the public health and economic impact of the coronavirus pandemic will keep markets extremely volatile, making it likely we'll touch a wide range of price levels in the months ahead. Amidst such uncertainty, it's a...

You're probably familiar, at least in passing, with the 'convexity' of long-term bonds - i.e. that yields dropping 1% produce a bigger price move than yields rising 1%. A significant amount of brainpower has gone into understanding all the ramifications of this convexity in the fixed income...

Continuously rebalanced long-short trades are similar to highly levered trades in that their PNL profile depends not only on the final distribution of return, but also on the realized co-variance structure of the asset pair. It's easily possible for both orientations of a rebalanced long-short...