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We propose a two-step hybrid investment strategy suitable for pension funds. Our method consists of an active component (an optimization-based approach to decide the asset allocation), followed by a passive strategy (an index-based approach). We test our strategy with data from the Chilean pension system using two different risk metrics and we show that our approach, in three out of five cases, yields results that are better than those generated by the Chilean fund administrators. In the two cases where our approach underperformed we show that it was the result of excessively tight constraints set up by the regulator.

Auction-house guarantees are becoming a common feature in the art market. We analyze these guarantees within the framework of financial options. This approach allows us to derive analytical (closed-form) expressions to value these positions, considering both, the case in which the painting is sold, and the case in which the painting goes unsold (“bought in”). In addition, we present several risk metrics that are useful to describe from an intuitive viewpoint the exposure of the auction house, and that of a third party (in case the auction house decides to layoff, fully or partially, the risk associated with offering such guarantees). We demonstrate that the expressions we derive satisfy the put-call parity relationship, and we further validate these formulas with a Monte Carlo simulation applied to a realistic example. We also show that the risk associated with such guarantees is lower than what is commonly believed by market practitioners, and we expose the dangers of relying on the Black-Scholes model to value such guarantees. Finally, having explicit expressions to assess the risk involved in these guarantees helps to bring more transparency to a notoriously opaque segment of the art market.