Question: replication using risky asset, risk free asset, and derivative position

[Studyguy]

Please clear something up for me:
If I’m given this equation: risky assets + derivative = risk free asset
Does this mean:
1) long position in risky asset, meaning buy at t=0 and sell at t=T
2) long position in derivative, meaning buying a forward that is executed at t=T
3) long position in risk free asset, meaning lend out funds until t=T, earning Rf
If this is true, can someone please explain the intuition behind this? Also, how thoroughly are we supposed to know this for the exam?

 

[Studyguy]

Bump.. Please help!

 

[S2000magician]

You have a long position in a risky asset and a short position in a forward contract on that risky asset.
From the time you enter into the forward until it expires you earn the risk-free rate.
At the end you’re left with cash; you’ve sold the risky asset.

 

[finact]

Look up put-call parity and make sure that makes sense.
The intuition is that you only get compensated for risk at the portfolio level. So while the future (or synthetic future) will be risky and the asset will be risky the portfolio of the two is not since they have perfect negative correlation.
In practice or in specific markets this isn’t so clean. An example would be the convience yield in the commodities market, or the change in dividend yields from expectation in a long position, or the short interest on an equity short position.