Tuesday, March 27, 2007
Heat Diffusion
The following is just note for my future reference.
Heat diffusion equation is closely related to the financial market. The Black-Scholes equation for option price is just a partial differential equation (PDE) which can be mapped into the Heat diffusion equation which occur backward in time. The Dupire equation is another PDE to determine a unique local volatility function that made the underlying process fit the volatility smile.
The emerging markets debt (Asia 2000) was also modeled by similar equations.
I don't have enough information to construct a model detail enough to calculate for the US sub-prime mortgage problem. But, at least, I believe it can't be something that can be confined.
Heat diffusion equation is closely related to the financial market. The Black-Scholes equation for option price is just a partial differential equation (PDE) which can be mapped into the Heat diffusion equation which occur backward in time. The Dupire equation is another PDE to determine a unique local volatility function that made the underlying process fit the volatility smile.
The emerging markets debt (Asia 2000) was also modeled by similar equations.
I don't have enough information to construct a model detail enough to calculate for the US sub-prime mortgage problem. But, at least, I believe it can't be something that can be confined.
Monday, March 05, 2007
Real Time Investment Experiment
I am still looking for an optimal investment solution.
I have 3 different experimental portfolio.
Set A is a group of more than 10 equitites funds, mainly Emerging Markets and European funds, and gold fund as alternative investment. I seldom make change but a strong negative edge would trigger a trade; this time I converted 30% of the funds to bond fund. The average return of it is about 20% per year over the past 5 years. The total operation cost is about 2% a year, including all setup and management fee.
Set B is a group of very aggressive funds, some are leveraged index fund. 2% of the investment in put options which I took as "investment cost". After deducting the cost, the annual return is just slightly higher than set A. The total operation cost, if include the cost for put options, is about 6% a year.
Set C is a balanced setup with only 3 funds, recommended by my new financial advisor. The total operation cost is about 2.5% a year. I would compare the set with my other portfolio.
In the recent Chinese crash, set A got about 5% lost off the peak, set B lost 2%, and set C lost 8%. In this down time, the put options of set B turn out to have huge profit and offset the lost. Set C consists of too few funds and a slump in India caused a significant set back.
Thursday, March 01, 2007
At a Turning Point
The movement in Yen looks interesting. It's seems that we are at a turing point. The trend for previous months' is over. I would rather stand aside until there is another clear trend develop.
I have switched my Europe and Emerging market funds to Bond fund. So, I have about 30% of investment in safe item. My put options made some profit, that's enough to protect my some of my long position.
A market sell-off is a good time for a check. Did individual mutual fund I own take too much risk and fall much more than corresponding index? Did the overall portfolio take too much risk ?
Next, what to buy ?
I have switched my Europe and Emerging market funds to Bond fund. So, I have about 30% of investment in safe item. My put options made some profit, that's enough to protect my some of my long position.
A market sell-off is a good time for a check. Did individual mutual fund I own take too much risk and fall much more than corresponding index? Did the overall portfolio take too much risk ?
Next, what to buy ?
