Negative holding of an asset

[Aisha]

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?

 

[mugono]

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?

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.

 

[Joe Hook]

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.

 

[AKS01]

Hi,

In April 2021, Q3 (iii) it says that if short selling was permitted for two positively correlated assets, the risk/variance would most certainly be reduced.
Why is that the case? How does short-selling allow them to reduce the variance?

 

[John Potter]

Groworanges.plc and Sellorangejuice.plc have shares with positively correlated returns. As a bonus question, can you suggest why? ;-)

When one of them does well, the other one also does well.
When one of them does badly, the other one also does badly.

So, if I have positive holdings in both then it could be a disaster! I have lots of risk

Instead...
I have 10 shares in Groworanges.plc
I have also short-sold 10 shares in Sellorangejuice.plc

If Groworanges.plc does well, I win but it also means Sellorangejuice.plc does well, so I lose. Overall, I do OK
If Groworanges.plc does badly, I lose but it also means Sellorangejuice.plc does badly, so I win. Overall, I do OK

So, my portfolio is going to do OK, overall, whatever happens. My risk has gone down.

Good luck!
John