Synthetic cash positions

Synthetic cash positions involve holding the underlying and shorting contracts to hedge the position in such a way that the hedged position earns the risk-free rate over the hedging period. (Dividends are reinvested in shares). Does “holding the underlying” mean we hold cash positions in risk free-bonds?

no it means holding the stock in question, then shorting it using futures to monetize your position.

So when you say monetize the position does that mean holding the margin required for the short futures in a risk free asset? Thus this margin earns the risk-free return.

That’s the collateral yield. Since you hold the underlying, then you will earn the risk free rate by the time the contract expires, because you’ve fixed in a forward price from the current spot price equal to the risk free rate.

You can also borrow against this position, and invest in something else entirely.

So when you say monetize the position does that mean holding the margin required for the short futures in a risk free asset? Thus this margin earns the risk-free return.

[/quote]

Since you hold the underlying, then you will earn the risk free rate by the time the contract expires, because you’ve fixed in a forward price from the current spot price equal to the risk free rate.

[/quote]

Sorry i’m unclear. How do we earn the risk free rate here?

Not quite sure on this one, but I’d assume you’re earning the risk free rate here since your collateral is usually held in t-bills or some risk free rate measure. Thus, if you’re long the underlying and short the future, you’re simply earning the collateral yield (the risk free rate).

Somebody correct me if I’m wrong

correct. In the curriculum you are always earning this risk free rate. Though in reality in recent years it’s 0. but whatever i guess makes it easier for us.

You have stock APPL, at a price of $100, you don’t want to hold apple anymore because you think the stock is a pretty bad bet, however you’re not sure yet if there are other good opportunities, so you intend to temporarily turn the stock to cash while still being yours.

You enter short into a 1-year APPL forward contract, if the risk-free rate is 1%, and the price F0 = $101. Now what happens is that you are effectively earning the risk free rate. If after one year the stock goes to zero, you get:

  • 101/100-1 = 1%

If the stock is a winner and goes to $200, you get:

  • 101/100-1 = 1%

In either case, you’ve earned the risk free rate, whether by delievery in exchange for cash, or by net cash settlement and still holding the underlying.

You can also borrow against your position, since you are effectively holding $101 in cash one year from now, so you borrow at a LTV ratio of 0.7, or $70 at 2%, invest that money in GOOGL, the stock goes from $70 to $80, sell it, pay back the $70+1.4, and pocket in a total profit for the year of

  • $1 + $10 - $1.4 = $9.6

Your EAR is 9.6%