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Negative holding of an asset

Discussion in 'CM2' started by Aisha, Oct 18, 2019.

  1. Aisha

    Aisha Very Active Member

    On page 14 of chapter 6 , it is written that if the correlation coefficient is 1, then there exists a risk free portfolio with V=0 for negative holding of SB and a positive holding of SA. Here EA=4% VA = 4%% and EB= 8% and VB=36%%
    I do understand that if there is negative holding of SB ( having much higher variance) the variance of the portfolio would drop and Also it can be adjusted in a way such that the positive variance of SA ( arising from positive holding of SA) can be neutralized to a zero variance.
    But I want to know, that in real world , what do we actually mean by negative holding and does it really help to achieve risk free portfolios if there is perfect positive correlation?
     
    Aisha, Oct 18, 2019
    #1
  2. mugono

    mugono Ton up Member

    Hi Aisha

    Another name for the negative holding of an asset in the real world is 'short selling'. This is a term used to describe a speculator selling an asset they do not own (in the hope that the price drops and they can buy it back at a lower price).

    If two assets are perfectly correlated, simultaneously buying one and selling the other would result in a gain in the asset you are long / short being exactly offset in a loss in the asset you are short / long.

    This is known as a 'box'* position. In a world where there is no arbitrage this box position would need to earn the risk free rate.

    If this wasn't the case an arbitraguer could earn a riskless profit by buying / selling the 'box' and selling / buying a bond.

    Hope that helps.

    *think of a box position as a zero coupon bond.
     
    Last edited: Oct 19, 2019
    mugono, Oct 19, 2019
    #2
  3. Joe Hook

    Joe Hook ActEd Tutor Staff Member

    Hi Aisha,

    A negative holding is indeed known as "short-selling" and refers to a position where you have sold rather than bought an asset. With a share, for example, you could borrow the share from the market, with an agreement to return it at a fixed future date, and sell it in the market at today's price. As you have sold the share on you will need to buy a share in the future to return it to the borrower. As an example:

    Today: Borrow the share and sell for market price (£2.80)
    End of contract: Buy a share from the market (£2.50) and return to the borrower

    On this investment you have made a 30p profit as you were able to sell at £2.80 but buy at £2.50 at a future date.

    If your portfolio had contained one positive holding of a share and the one negative holding of the share the two investments cancel out. You may have also heard this called a hedging portfolio. If your portfolio/position is hedged it means that it is not exposed to price movements (movements on the various elements will cancel out) and so the portfolio is risk-free. If your assets were perfectly negatively correlated then buying both would also create a risk-free portfolio

    Short-selling occurs more frequently later in the course in proofs and questions requiring you to construct hedged portfolios so do not worry too much if it seems a little unclear in Chapter 6.
     
    Joe Hook, Oct 21, 2019
    #3

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