P1.T2.305. Minimum variance hedge (Miller)


New Member
Hi @David Harper CFA FRM I wasn't sure where to put this question since it's related to instruction video slides, I apologies if it caused inconvenience. But I haven't really understood the concept of using Price relative formula & LN daily return. Can you please put in some explanation to this.

Ch= Random Variables Presentation Slide (Page # 13)



David Harper CFA FRM

David Harper CFA FRM
Staff member
HI Navjyot (@navjyotbirdy) When the daily price increases from 10.00 to 10.73, there basically two ways to compute the return:
  • 10.73/10.00 - 1 = 7.30% where 10.73/10.00 is a "price relative" (aka, wealth ration). This is a discrete holding period return (HPR), or
  • ln(10.73/10.00) = 7.046% which is a continuously compounded log return. My example assumes there are no dividends received during the intraday period.
As this is super basic with extensive forum conversation already, I must be brief (use search, see my youtube video section). Hopefully others can add color. The one thing I will say is: neither is wrong, but:
  • the continuous log returns are time-additive. This is really helpful. We can just add the daily returns!
  • the discrete (aka, simple) returns are cross-sectional additive. We can add the asset/component returns of each asset in the portfolio for the portfolio's one day return.
One of my very first YT videos is below and tries to explain why log returns are time additive but not portfolio additive. Yikes, I hate my older YT videos. I hope that's a good start.