There is no way I'm going to be able to explain how to build regression models. What I tried to do was just offer the simplest model (100%
CAPE + static bond return - static expenses).
I rattled off a few of the many simplifying assumptions inherent in this model. Since the model does not fit the actual performance figures, some of those assumptions must be wrong. One way to figure out which ones is to relax (weaken or remove) some of the assumptions and try fitting the resulting, more complex model to the data.
While it may look like you've got lots of data points to work with (each day's performance), there's lots of noise inherent in that data, especially since you've no real idea what's going on with the bond portion (more below). There are various standard filtering/smoothing techniques that can be tried to deal with this. The end result, while cleaner, would leave you with too sparse a data set to fit to most models. (Call that intuition from experience, I haven't worked the numbers.)
While DoubleLine may say that the bond portion has returned a fairly steady 2.87% annually, it's not clear whether that is net or gross, or what portion of the portfolio the bonds represent ("up to 100%"). One sees, e.g. at least 7% of the fund in cash (so add that to the model). One doesn't even need M* to see the cash. In the
latest (semi) annual report, the fund had 7.8% invested in three MMFs (Blackrock Liquidity FedFund, Fidelity Institutional MM, Morgan Stanley Institutional).
Nor is the bond return all that steady. In that same semiannual report, the six month contribution of the bond portion is reported to be 2.3% (not annualized). Annualized, that's 4.65%, a far cry from 2.87%. How likely is it that they're fudging 2.87%? I'm sure that this is a reasonably accurate number. It's the "steady" part that's dubious. Not from a 100,000 foot level, i.e. the bond returns are not bouncing around like some EM bond funds. But it's hardly constant, certainly not close enough to build a model around that assumption.
Personally, I'm comfortable with my prior posts - that the fund should approximate
CAPE (for better or worse; I didn't comment on how that might behave) less overhead (leveraging costs, management costs, administrative costs, trading costs, clawback costs) plus bond portfolio returns (as much or as little a black box as one regards all of DoubleLine's bond funds).
Read the fund reports - they give the contributions from the
CAPE side and the bond side. Add these numbers, subtract the fund's ER, subtract a bit more for the stuff that isn't reflected in the ER, and you get the total return of the fund. That much is easy to confirm.