I am trying to build an automated monthly XIRR tracker for mutual fund SIPs with respect to a benchmark. This will help us understand how returns from a SIP can fluctuate and how consistently the fund has performed with respect to its benchmark. The automation is not yet complete but since I found a good a good SIP account statement generator since inception (link given below), here are some results for HDFC Top 200.

## Monthly XIRR tracking since inception (Sep. 1996)

Since XIRR is not reliable for investments less than a year old, XIRR data for the first 12 SIP installments is not included.

The graph suggests that although the XIRR tracks the general market movement, the fluctuations die down after 5+ years.

Correlation with NAV movement: Positive. About 34%

The fall during the 2008 crash is about 15% or so.

Let us look at the monthly XIRR had the SIP been started at each of the three arrows above.

## Monthly XIRR tracking since Jan. 2004

For a SIP started after the last bull run had begun, the fall during the 2008 crash is much higher ~ more than 20%. Here again the fluctuations die down after a few years.

Correlation with NAV movement: negative! Not sure how to interpret that.

## Monthly XIRR tracking since Nov. 2007

This is for a SIP begun right before the 2008 crash. Recall that XIRR data for the first 12 SIP installments is not included.

Correlation with NAV movement: Positive. 15%

## Monthly XIRR tracking since Oct. 2010

This is for a SIP started after the market bounced back after the 2008 crash.

Correlation with NAV movement: Obviously positive and large. 91%

**Impression:** Do the above graphs suggest that although the XIRR of a SIP investment broadly follows market movements, its volatility decreases with age? For all our sakes, let us hope so.

Here is a similar study for Franklin Blue Chip: **Tracking a mutual fund SIP: Month by month XIRR**

The automated tracker can only analyze investments from 3rd April 2006. I will add a comparison with a lump sum investment.

The SIP account statements for this post were generated using this SIP calculator

http://www.bluechipindia.co.in/MutualFund/MFInner.aspx?id=7

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Arun VasanHello sir,

Very interesting. This answers some questions that were bugging me about investing in a SIP during high PE periods. Essentially, the initial state of the system doesn't seem to matter so much as the final state for the XIRR calculation. Ideally, your final state would be decided a decade later, and triggered as a re-balancing when the market is in high PE zones. In any case, the XIRR seems to be lower bounded when averaged over a rough market cycle (of 5 years).

Regarding your comment about the negative correlation, assuming you are calculating the regular pearson values, I would guess it is to be expected. The data you have is one sample path of (very likely non-stationary) stochastic processes (NAV and XIRR), not really independent samples from the joint distribution of two (stationary) random variables (NAV and XIRR).

Thanks very much. I enjoyed reading this.

Regards,

Arun

Arun VasanTo add to the point above, I was assuming that the SIP investments would increase yearly. If the SIP installment is constant, essentially, you have only one non-stationary process, the NAV, and the XIRR which is a function of all the past NAV's alone. So it's very likely the non-stationarity in the NAV itself, which causes the negative correlation.

Arun VasanHello sir,

Very interesting. This answers some questions that were bugging me about investing in a SIP during high PE periods. Essentially, the initial state of the system doesn't seem to matter so much as the final state for the XIRR calculation. Ideally, your final state would be decided a decade later, and triggered as a re-balancing when the market is in high PE zones. In any case, the XIRR seems to be lower bounded when averaged over a rough market cycle (of 5 years).

Regarding your comment about the negative correlation, assuming you are calculating the regular pearson values, I would guess it is to be expected. The data you have is one sample path of (very likely non-stationary) stochastic processes (NAV and XIRR), not really independent samples from the joint distribution of two (stationary) random variables (NAV and XIRR).

Thanks very much. I enjoyed reading this.

Regards,

Arun

Arun VasanTo add to the point above, I was assuming that the SIP investments would increase yearly. If the SIP installment is constant, essentially, you have only one non-stationary process, the NAV, and the XIRR which is a function of all the past NAV's alone. So it's very likely the non-stationarity in the NAV itself, which causes the negative correlation.

kalyanKeeping maths aside, when you are running a sip for a long time, most of the fund value would have been invested long time back. So the xirr will be following the long term yields. A newer sip will have most of its fund value recently. Obviously for a MF the daily NAV will be most volatile and the 5 years sliding yield will have less variation. The xirr should follow the market but less violently like a long term yield for a MF.

The risk is still there. Just beacause you have a xirr of 13 doesnt mean you stay there. You will still go to 9 or 17 but more steadily than violently. On the same note I assume for the sips that increase amount every year the variance of xirr increases and the variance depending on the %increase you do in SIP.

freefincalPost authorYes, that is what the math shows! So no need to keep it aside 🙂

kalyanKeeping maths aside, when you are running a sip for a long time, most of the fund value would have been invested long time back. So the xirr will be following the long term yields. A newer sip will have most of its fund value recently. Obviously for a MF the daily NAV will be most volatile and the 5 years sliding yield will have less variation. The xirr should follow the market but less violently like a long term yield for a MF.

The risk is still there. Just beacause you have a xirr of 13 doesnt mean you stay there. You will still go to 9 or 17 but more steadily than violently. On the same note I assume for the sips that increase amount every year the variance of xirr increases and the variance depending on the %increase you do in SIP.

freefincalPost authorYes, that is what the math shows! So no need to keep it aside 🙂