Author: shyam

Allocating a Two-Asset Portfolio

Asset allocation and diversification are considered to be the holy grail of investing. Adding non-correlated assets to one’s portfolio is supposed to reduce volatility and hence encourage the good behavior of staying invested through market cycles. Here, we look at a simple two asset portfolio and work through some simple scenarios.

Picking the Assets and Allocation

When one looks historical inflation adjusted returns (link,) an investor with a 10+ year horizon should be invested in midcaps. So we pick the NIFTY MIDCAP 100 index and the 0-5 year bond total return index as the assets for our simple allocation setup.

The most popular allocation for an equity/bond portfolio in literature is 60/40 in favor of equities. However, we will go through a range of scenarios where the equity allocation is stepped through from 40% to 90% in increments of 10%

After picking the assets and their allocation, we need to figure out what would trigger a rebalance. Should we rebalance whenever the weights go off by 5% or should we wait until they drift 20% from their initial allocation? We will step through this as well – from 5% to 100% in increments of 10%

And lastly, the question of capital gains and securities transaction tax. Tax incidence on these two asset classes have varied over time. So for simplicity, we will assume an STT of 0.1% and a capital gains tax of 10% applied whenever a rebalance occurs.

The results

As one would expect, higher the risk taken, higher the cumulative returns. What changes are the drawdowns. Here are the various allocations, assuming a 20% rebalance threshold and with/without the tax drag. Note the different drawdown profiles at the bottom of the chart.
Without taxes:
equity/bond with 5% rebalance threshold (no tax drag)
After tax:
equity/bond with 5% rebalance threshold (no tax drag)

And here are the historical returns of the 60/40 portfolio:

pre and post tax returns of a 60/40 equity/bond portfolio
As intuition would suggest, the more frequently you rebalance, the higher your tax incidence. But keeping the rebalance threshold too high would allow a single asset to balloon and make the portfolio too sensitive to it. As show in this table, historically, keeping a rebalance threshold at 20% has worked out well for a 60/40 equity/bond portfolio.

Code, charts and the complete result dataset are available on github.

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Mutual Funds: A quick note on performance metrics

There is absolutely zero stability in metrics used to analyze mutual fund performance. Whether it is alpha, beta or information ratio, they all vary over time and across market environments. Using them to pick the next “winning” fund is pointless. They are, at best, a measure of what happened in the past.

We take a 200-week sliding window of midcap mutual fund returns and calculate its alpha, beta and information ratio. Here’s how these numbers stack up for the HDFC Mid-Cap Opportunities Fund.
HDFC Midcap fund

What is apparent here is that

  1. There is no case for dropping a fund because of declining alpha. Alpha keeps changing through time.
  2. You cannot escape negative beta.
  3. Managers seem to be able to outperform on the way up but not under-perform drastically on the way down. This is asymmetric risk/reward for those who can stick with investments through long periods of time.
  4. Some argue that recent SEBI regulations on mutual fund holdings will erode alpha. Only time will tell if that is true because of (1) and (2).
  5. Under-performance is not permanent. See ICICI’s fund below.

ICICI midcap mutual fund

What we see here is that at least in the midcap space, funds have been able to outperform the index in the past (both recent and distant.) However, that is no guide to the future.

Notes:

  • The total-return index doesn’t go back long enough to be used for this analysis.
  • The risk-free rate used was the 0-5 year YTM adjusted for the weekly time-series.

Code, charts and time-series alpha, beta and IR for about a dozen mutual funds that are over 10-years old are on github.

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Daily vs. Monthly SIP

We recently ran some numbers against some typical “buy the dip” strategies and concluded that they do not result in any significant advantage over a daily SIP. The daily SIP base case was chosen because it is easy to compute. It was not a recommendation for investors to switch over their monthly SIPs to daily ones.

Barring a few outliers, over rolling 5-year windows, a daily SIP and a monthly SIP result in similar amounts of assets accumulated at the end.
daily vs. monthly sip

Related links:
Systematic Buy-the-Dip, an Update
Systematic Buy-the-Dip, SMA crosses
Trading Day of Month Returns

Code is on github.

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Systematic Buy-the-Dip, SMA crosses

Previously, we looked at a dip buying strategy based on how low an index is trading below its peak. We now run some numbers against another popular strategy: the SMA crossover.

Introduction

Everybody wants to buy markets that are trending up. When a lower SMA (say, 3-day) crosses an upper SMA (say, 200-day) an uptrend is identified. What if one only buys when such a crossover occurs? What if one accumulates cash otherwise and collects interest while waiting for such crosses?

The following chart shows the periods in which NIFTY is below the upper SMA in red. Purchases are shown as green dots.
NIFTY cross-over

Here’s the one for the small-cap index:
small cap cross over

Results

We calculate the min, max and mean difference in the final amount of the index accumulated over rolling 5-year periods. The second column in the table below is the lower SMA used in the cross-over.
difference in assets accumulated

When it comes to small-caps, there are some configurations where, on average, the cross-over strategy accumulates more assets. However, investors are taking a risk where they could encounter 5-year periods where there is a shortfall in assets by an equal amount.

Waiting for the dip using this strategy is not a good idea compared to a simple daily SIP.

Note that we define success as the terminal value of the number of units of the index purchased. This is different from each unit being profitable.

Code is on github.

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Systematic Buy-the-Dip, an Update

We had looked at the difference between buying the dip vs. a daily SIP back in June-2016 (link.) The following is an update and an expansion of the same idea.

Introduction

Everybody wants to “buy the dip.” We wanted to run some numbers against what investors would typically do if they were to follow such a strategy.

  • We invest Rs. 1 every day the market is open.
  • For SIP, we buy Rs. 1 of a particular index.
  • For DIP, we either invest in cash or we liquidate the cash account and buy the index (if there is a ‘dip’), and we continue to invest Rs. 1 in the index as long as it is in DIP.

To define a DIP, we need two things.

  1. The look-back (formation) period over which percentage loss from peak is observed.
  2. The threshold percentage loss from peak.

The scenario will continue to be in DIP as long as the index is trading a threshold percentage below its peak.

The following shows the periods in which the NIFTY was purchased in red. The look-back period was 100-days and the threshold was -10%. This translates to “buy the index only when it is trading 10% below its previous 100-day peak.”

NIFTY buy the dip

Here’s the one for “buy MIDCAP only when it is trading 15% below its previous 200-day peak.”
MIDCAP buy the dip

We expand on our previous attempt by adding more indices and running the scenario through rolling 5-year periods. We then compare the terminal value of the number of units of the index purchased under DIP with SIP.

Results

buy the dip results

There are very few scenarios where DIP buying is better than SIP buying. This happens to the NIFTY when you buy it when it is trading 20% below its 100/200/500-day peak. However, this is “on average.” There were 5-year periods when DIP buying would have resulted in about 5% less assets than SIP buying under the same lookbacks.

Hence, we reassert our previous finding that waiting for the dip is not a good idea compared to a simple daily SIP.

Note that we define success as the terminal value of the number of units of the index purchased. This is different from each unit being profitable.

Code is on github.

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