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Perpetual Tracker with Risk Target

Submitted by cahn on 21 June, 2009 - 5:07pm

Perpetual Tracker with Risk Target ("Perpetual+") is an investment process with the following objectives:

  • Manage the portfolio with a fixed risk target (risk target being defined as the realised volatility)
  • Ensure a certain percentage of the highest reached portfolio value is protected on a perpetual basis

The process is a version of the Time-Invariant Portfolio Insurance ("TIPI") technique and defines the Multiplier (a measure of riskiness of the portfolio) as a function of the realised volatility of the portfolio, reflecting the view that the riskiness of an underlying is not constant.

I have been running a process since 19 May 09 on Hang Seng China Enterprises Index ("HSCEI"). The process switches between the index and the overnight money market depending on

  • The distance between the portfolio and the targeted protection
  • The 30-day realised volatility of the index

Below are the specification of the process:

  • Protection ("BF"): 70% of the highest reached portfolio value ("RPV")
  • Multipler: Min(8, 8 x Vol Target / 30-day Realised Volatility)
  • Vol Target: 15%
  • Rebalance Tolerance: +/-10%
  • Maximum exposure to HSCEI: 240%
  • Minimum exposure to HSCEI: 0%
  • Initial portfolio value: $500,000

What did I say then?

Composite asset - necessary adjustments

Submitted by cahn on 17 January, 2008 - 3:11pm
Posted in

Assume $ S_t $ in $ FX_t^{h} $ follows $ dS_t=\mu_{h}S_tdt+\sigma_{s}S_tdW_t $ and we have a foreign currency, $ FX_t^{a} $, with the corresponding $ \mu_{a} $, $ \sigma_{fx_{h}fx_{a}} $ and $ \rho_{s,fx_{h}fx_{a}} $.

A composite asset of $ S_t $ into $ FX_t^{a} $, $ S_t^{a} $, is then

\[<br /> dS_t^{a}=\mu_{a}S_t^{a}dt+\sqrt{\sigma_{s}^2+\sigma_{fx_{h}fx_{a}}^2+2\sigma_{s}\sigma_{fx_{h}fx_{a}}\rho_{s,fx_{h}fx_{a}}}S_t^{a}d\acute{W}_t\]