Tag: allocation

SIP: Expected Returns

“A monthly Rs. 5,000/- SIP will make you a crore-pathi!” Screamed a Facebook ad. Really? Is it that simple? Lets break it apart and find out the assumptions baked into that bold assertion.

Historical annualized mid-cap returns

annualized historical midcap 100 returns

The NIFTY MIDCAP 100 index has given an annualized return of ~21% between 2002 and 2016. If you assume a 20% return over the next 20 years, then a monthly SIP of Rs. 5,000 will indeed result in a Rs. 1,21,94,282/- corpus, making you are crore-pathi.

But what happens if you were 100% invested in Midcaps (20% returns!) and retired in 2007? All your crore-pathi dreams would have gone poof (Midcaps crashed 60% in 2008.)

Static Asset allocation

One way to mitigate blow-up risk is to diversify away from equities into bonds. A popular allocation scheme is the 60/40 equity/bond allocation. So how much should you expect a 20 year, Rs. 5,000/- monthly SIP to return under this scheme?

SIP returns

It is a range of returns because it looks at a 10,000 random samples of 20×12 monthly (historical) returns to reflect the path-dependency of SIPs.

Now, what about the size of the final corpus under this scheme?

SIP returns

On average, you should not expect more then Rs. 60 lakhs as the final corpus under a static 60/40 allocation scheme. You could get unlucky and end up with Rs. 30 lakhs or get very lucky and end up with Rs. 1 crore. But this is the expected range of returns.

If you still want to get to the magic one-crore mark, you will have to “step-up” the SIP contributions.

The final corpus if the SIP is Rs. 5k a month for the first 5 years and 10k, 15k and 20k for the next 5 year blocks, under a static 60/40 allocation:
SIP returns

Glide-path Asset allocation

The 60/40 split would still leave you exposed to market downturns towards the end. One way to eliminate most equity market risks is to adopt an asset allocation scheme that starts with 100% equity, 0% bonds and “glides” to 5% equity and 95% bonds over a period of 20 years. This way, you will have progressively less exposure to equity as you near the end. Under a fixed Rs. 5,000/- a month SIP, your final corpus is likely to be:

SIP returns

And what if you stepped it up?
SIP returns

Take-away

The kind of “straight-line” thinking that the ad propagates will set you up for disappointment if you don’t understand the underlying assumptions that went into it. Prudent asset allocation is much more than raw performance. It is making sure that you will have the money when you need it. And it inevitably compresses returns, so it requires you to save more.

Next time you see such an ad, you can respond by saying “Give me one crore now and I will give you 5k every month for the next 20 yrs.”


Notes:
Rebalanced once a year.
Allows the allocation to drift by 5% before triggering a rebalance.
Assumes a 10% tax on returns at every rebalance.
“0_5” is the total return index of the 0-5 year government bond.

Code and additional charts (with returns using the NIFTY 50 index) are on github.

Asset Allocation

Introduction

How does an equity/bond 2-asset portfolio look like?
Read: Allocating a Two-Asset Portfolio

A three asset portfolio

Indian midcaps + bonds with Nasdaq-100 ETF. Is there a benefit to using portfolio optimization algorithms after taxes and transaction costs are taken into account?
Read: Allocating a Three-Asset Portfolio, Equal Weighted and Allocating a Three-Asset Portfolio, Optimized

Adding gold into the mix

Does gold have a role to play in a systematic, diversified portfolio?
Read: Allocating a Four-Asset Portfolio

Investing in a systematic, diversified portfolio

A ready-to-invest Theme, the EQUAL-III, that takes care of keeping track of everything.
Read: The EQUAL-III Theme

Expected Returns

What are the range of expected SIP returns under prudent asset allocation schemes?
Read: SIP: Expected Returns

The EQUAL-III Theme

Our recent series on asset allocation walked through how different investment decisions affect portfolio returns and risk.

  1. Number of assets: Three is better than two and four.
  2. Rebalance threshold: Allowing a single asset to drift upto 80% reduces transaction costs and taxes.
  3. Weighing scheme: Equal weight is better than portfolio optimization methods.

You can read through the posts and the various factors that went into the analysis in order:

  1. Allocating a Two-Asset Portfolio
  2. Allocating a Three-Asset Portfolio, Equal Weighted
  3. Allocating a Three-Asset Portfolio, Optimized
  4. Allocating a Four-Asset Portfolio

For investors looking to gain from such a portfolio, we have setup a ready-to-invest Theme, the EQUAL-III, that takes care of keeping track of everything. It maintains an equal-weight portfolio of the M100 (Midcap-100 ETF,) N100 (Nasdaq-100 ETF) and the RRSLGETF (Long Term Gilt ETF.)

Questions? WhatsApp us +91-80-2665-0232

Allocating a Four-Asset Portfolio

Our previous posts showed how various allocation decisions impact optimized and equal-weighted three-asset portfolios. Here, we add a fourth asset – gold – and run it through the same scenarios.

Picking the Assets and Allocation

The assets we selected previously – MIDCAP, 0-5yr bond and NASDAQ-100 – were based on low observed historical pair-wise correlations. Most investors tend to add a fourth asset – gold – to their portfolios. Not only is gold not correlated with the other three, it has the added benefit of being priced internationally but traded locally. This allows it to benefit from rupee depreciation even if international gold prices remain flat. Observe how, at times, gold has a negative correlation to other assets:
correlations between gold, SPY, QQQ, MIDCAP and BONDs

The results

In the cumulative return and drawdown chart below, A1 is the MIDCAP index, A2 is the 0-5yr bond index, A3 is the QQQ and A4 is gold. A tax drag of 10% and an STT of 0.1% is applied at every rebalance. The rebalance threshold is set at 20%. The light-blue lines are the resulting portfolio returns. In the case of optimized portfolios, assets are allowed to have a weighting between 10% and 40% during the optimization process.

Equal Weighted

after tax cumulative returns of 4-asset equal weighted portfolio

Variance optimized

after tax cumulative returns of 4-asset variance optimized portfolio

Expected Tail Loss optimized

after tax cumulative returns of 4-asset ETL optimzied portfolio

Pre- and Post-tax returns

before and after tax cumulative returns of 4-asset equal weighted portfolio
before and after tax cumulative returns of 4-asset variance optimized portfolio
before and after tax cumulative returns of 4-asset ETL optimized portfolio

Rebalance

The rebalance threshold ends up determining the frequency of rebalance events. For a variance optimized portfolio, contrast the difference between a 20% threshold and an 80% threshold:

4-asset portfolio at a 20% rebalance threshold
4-asset portfolio at a 80% rebalance threshold

Take-away

  1. Every time there is a rebalance, the tax-man cometh and taketh away. Trying to minimize taxes is equivalent to minimizing the number of rebalancing events.
  2. To minimize reblancing events, one could set the threshold of rebalance higher. But there is a point of inflection with regards to after-tax returns.
  3. Allowing a single asset to balloon in weight risks larger portfolio drawdowns if that asset deflates.
  4. A four-asset equal weight portfolio under-performs a 3-asset equal weight portfolio. Gold maybe a good diversifier, but it doesn’t appear to do any favors to the portfolio on the performance front.
  5. Equal-weight 4-asset portfolio containing gold (above) drew-down less than the equal-weight 3-asset portfolio during the 2008 carnage (~30% vs. ~40%, respectively.)

Adding gold to a portfolio does not look like a good idea when looked through the lens of asset allocation schemes discussed here. However, there is a strong case for owning gold and the Sovereign Gold Bond (SGB) Scheme makes a lot of sense. See our previous post regarding the case for owning gold in India here.

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

Allocating a Three-Asset Portfolio, Optimized

Our previous post showed how various allocation decisions impact an equal-weighted three-asset portfolio. However, equal-weights are not the only way to go. Every time a rebalance occurs, we can use that opportunity to re-weight the assets to minimize expected risk while maximizing expected returns. In this post, we look at two ways in which risk and returns can be optimized.

Portfolio optimization and the efficient frontier

The intuition behind what we are going to do is quite simple: for a given set of assets, there is an ideal mix of them that perfectly balances risk with reward. Imagine a plot of risk and returns of each asset under consideration. Harry Markowitz showed back in the 1950’s that they form a parabola and at a particular tangent of the parabola lies the ideal mix. The goal of portfolio optimization is to find that point. Here are some links that explain this concept further:

For the purpose of this post, we will assume risk to either mean variance (var) or expected tail loss (ETL.) We will use portfolio optimization methods to minimize one of these risk metric and maximize expected mean returns below.

Optimized portfolios

Like before, to keep things simple, we will go with the MIDCAP 100 index (A1), the 0-5yr TRI (A2) and the QQQ ETF (prices converted to INR, A3) as the three assets that form our portfolio.

Here is how the optimized minimum-variance portfolio performs after-tax:
min-var 3-asset portfolio (NIFTY MIDCAP, 0-5yr bond, NASDAQ-100)

Asset weights after rebalance:
min-var 3-asset portfolio (NIFTY MIDCAP, 0-5yr bond, NASDAQ-100) asset weights

And here is how the optimized minimum-ETL portfolio performs after-tax:
min-etl 3-asset portfolio (NIFTY MIDCAP, 0-5yr bond, NASDAQ-100)

Asset weights after rebalance:
min-etl 3-asset portfolio (NIFTY MIDCAP, 0-5yr bond, NASDAQ-100) asset weights

Min-var portfolio returns

min-var 3-asset portfolio (NIFTY MIDCAP, 0-5yr bond, NASDAQ-100) returns

Min-ETL portfolio returns

min-var 3-asset portfolio (NIFTY MIDCAP, 0-5yr bond, NASDAQ-100) returns

Take-away

  1. All things equal, the optimized portfolios under-perform the equal-weight portfolio in terms of absolute returns.
  2. Optimized portfolios show lesser risk than the equal-weight portfolio. During the 2008 carnage, for example, equal-weight drew-down ~40% whereas optimized portfolios drew-down ~20%.
  3. Optimized portfolios over-weigh bonds. Hard limits were set on the maximum and minimum weights the assets can have in optimized portfolios. Toggling these will have a significant impact on portfolio risk and returns.

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