Why use future value for synthetic positions

[firefirehelphelp]

Hi everyone,

Would like to clarify some points about synthetic positions:

1. Do we only use future value to compute the number of contracts required for synthetic positions? Based on reading these links (link 1, link 2) my guess is yes.
2. But why do we not use future value for other situations? For example, in scenarios such as the below:

Example: A manager of a $5,000,000 portfolio wants to increase the beta from the current value of 0.8 to 1.1. The beta on the futures contract is 1.05, and the total futures price is $240,000.

Note: I am aware you can argue that the risk free rate wasn’t even given so you can’t possibly compute a future value. But can we just assume the examiner chooses to be nasty and throws in the risk-free rate just to confuse us.

Thank you

[ju2tin]

Same question here! Would love to know the answer.

[ju2tin]

Okay, I think I have it figured out.

First of all, Schweser on the same material specifically says that synthetic positions are more precise, so they use future value, while other positions (like for asset allocation) do not. Seems weird, but that’s what they say.

Second, this Schweser approach is consistent with how CFAI treats the material.

– If the question says you are constructing a synthetic index or creating synthetic cash , that’s your signal that it’s a precise position and you need to use the future value.

– If the question talks about changing asset class allocations or adjusting beta or duration , then boom, you use present value.

The only apparent exception to the rule is CFAI EOC Question 8, which talks about creating synthetic cash but still uses present value. ಠ_ಠ

On the surface, Question 8 seems like Question 3, which also talks about creating synthetic cash, but uses the future value. I think the difference may be that Question 3 specifically says the transaction is risk-free. That may imply that they are being extra-precise and want you to show how the amounts involved are affected by earning the risk-free rate over time. Question 8 doesn’t say anything about being risk-free.

(Similarly, Question 2, which also uses future value, makes a big deal about asking you to show how the synthetic index earns the same return as an investment in the actual stock index. In other words, they want you to be precise.)

One more thing: If the question talks about pre-investing an amount of money to be received in the future, you just use that specified amount of money, which is already a future value.

[firefirehelphelp]

@ju2tin

Okay, I think I have it figured out.

First of all, Schweser on the same material specifically says that synthetic positions are more precise, so they use future value, while other positions (like for asset allocation) do not. Seems weird, but that’s what they say.

Second, this Schweser approach is consistent with how CFAI treats the material.

– If the question says you are constructing a synthetic index or creating synthetic cash , that’s your signal that it’s a precise position and you need to use the future value.

– If the question talks about changing asset class allocations or adjusting beta or duration , then boom, you use present value.

The only apparent exception to the rule is CFAI EOC Question 8, which talks about creating synthetic cash but still uses present value. ಠ_ಠ

On the surface, Question 8 seems like Question 3, which also talks about creating synthetic cash, but uses the future value. I think the difference may be that Question 3 specifically says the transaction is risk-free. That may imply that they are being extra-precise and want you to show how the amounts involved are affected by earning the risk-free rate over time. Question 8 doesn’t say anything about being risk-free.

(Similarly, Question 2, which also uses future value, makes a big deal about asking you to show how the synthetic index earns the same return as an investment in the actual stock index. In other words, they want you to be precise.)

One more thing: If the question talks about pre-investing an amount of money to be received in the future, you just use that specified amount of money, which is already a future value.

Hey ju2tin,

Thanks for the reply. I had a look at Question 8 and it indeed is strange especially since they provided the risk-free rate. Guess I would have to go with the logic your laid out in your post. Thank you once again.