0

I've been given a formula that has to do with the calculation of hedge position, but I'm struggling to understand it. I'm really new to financial Maths or financial in general.

The formula is: $\frac{-\beta_{asset} \times p_{asset} \times q_{asset}}{p_{spy}}$

Where $\beta_{asset}$ is the sensitivity of asset to the market, $p_{asset}$ is the price of the asset, $q_{asset}$ is quantity of traded assets in a portfolio and $p_{spy}$ is the price of SPY (S&P ETF).

I don't know exactly what that formula returns. Given its dimensionality it seems to be a quantity, but I don't know if it's a delta on the current's asset position.

What I'm asked for exactly is to use that formula to determine the current position in hedge instrument SPY required position and required adjustment.

Carlos Navarro Astiasarán
  • 101
  • 1
    The formula returns the number of shares of SPY required to hedge the 'asset'. In other words the formula returns the value of $q_{spy}$. The q's represent number of shares and the p's represent prices per share. A negative q means a short position. The $\beta$ is a known number, typically between 0.5 and 1.5, known as the Beta of the Asset. – nbbo2 Jul 12 '22 at 09:02
  • 1
    $p_{asset} \times q_{asset}$ is the market value of the asset in dollars. $p_{spy} \times q_{spy}$ is the market value of the SPY position. And to balance each other these have to be proportinal as shown in the equation $p_{spy} \times q_{spy} = -\beta \times p_{asset} \times q_{asset}$. (Which we can solve for $q_{spy}$).For example when beta is 1 each one thousand dollars of spy short counter-balances 1000 dollars of the asset. – nbbo2 Jul 12 '22 at 09:29
  • Thank you very much @nbbo2 for your clear answer, I really appreciate it. Another question: when should you 'trigger' this operation? I mean, say you have asset A (p=100, q=5, b=1.2) with p_spy=200. Then q_spy=-3, i.e., sell 3. If a minute after doing this the prices changes to 133, then q_spy=-4. Does this means I should sell 4 now? Or just the difference (1)? And what if instead of a price change I sell 2 of asset A? should I recalculate with q_assetA=-2? and finally, what if the p_spy changes a minute after performing the operation? should this be a trigger to operate too? – Carlos Navarro Astiasarán Jul 12 '22 at 10:32
  • 1
    That's up to you. Generally you buy/sell SPY when you sell/buy any amount of the asset. That's the important thing. But you could also "review the situation" periodically (weekly or monthly, possibly even daily, but certainly not every minute) to make sure the position in the asset(s) and in SPY are matched. And make an adjustement to the SPY position if appropriate. – nbbo2 Jul 12 '22 at 12:04

0 Answers0