Should you be investing in Cryptos right now?

Amidst the COVID-19 pandemic, should you be adding the crypto eggs to your basket?

Due to a soured economic outlook induced by the global pandemic, cross-asset correlations, systematic risk and downside volatility of investment assets increased. This led to the simultaneous crash across assets in mid-March. Data analysis revealed that holding cryptocurrencies would have preserved wealth during the crisis. Furthermore, a rule of thumb 60:40 allocation across risky and safe haven assets¹ – which amounts to 30% for crypto – would have outperformed that generated from a Markowitz optimisation² of the portfolio’s Sortino ratio³ by around 1.4 times.

A global portfolio was constructed consisting of stock index ETF/futures (SPDR S&P 500 and Nifty 50), traditional safe havens (Gold futures and the Japanese Yen) and popular cryptocurrencies (Bitcoin and Ethereum). The performance of the portfolio was analysed for an 8 month period before and after the Covid 19 outbreak on 1st Dec 2019 – the day when it was identified in Wuhan, China. The tools used for analysis are the mean variance optimization framework, correlation, beta, Sharpe and Sortino ratios.


Cryptos as a safe haven – If cryptocurrencies were to qualify as safe havens, they would be expected to have low correlations⁴ with traditional risky assets and either maintain or increase in value during stressed market periods. Since the outbreak, the once negligible, negative correlations between the cryptocurrencies and stock indices have reversed in direction, increasing by 30-50%, that between Bitcoin and S&P 500 reached 53%. The betas reflect the same. The higher positive correlations led to increased portfolio risk. However, as shall be apparent by the end of this article, this does not rule out the case for adding crypto investments to the portfolio.

The Bitcoin-Altcoin connect – It is interesting to note that the correlation between Bitcoin and Ethereum increased further by 10%, from around 81% to 91%. This serves as a reminder that intra-crypto diversification – between Bitcoin and altcoins – should also be explored in future research since their correlations seem to increase during times of market stress.

Crypto trading implications – The increased correlations also have an important implication for standalone crypto trading. There is growing acknowledgement between crypto traders that cryptos are increasingly tracking the S&P 500 these days. This means that traders must also factor in the broader market sentiment in their trade decisions (for non-market neutral strategies).

The new relationships could also be used to counter the argument that cryptocurrencies do not have any fundamentals. One could argue, for example, that cryptos derive their values from international crypto transactions and an unfavourable economic outlook and a fall in consumer spending does not bode well for them.

Crypto allocation – Case A – Consider a rule of thumb 60-40 allocation to risky assets and safe havens, with an equal distribution within the two categories (15% across both the stock indices and cryptos, 20% across safe havens). Due to the increased correlations and market volatility, the downside portfolio risk increased by 2x. However, the return from the portfolio, led by the massive crypto returns and gold living up to its safe haven potential, increased by 2.3x. The Sortino ratio increased from 1.95 to 2.18, which is a decent result for an investment portfolio, especially during a stressed market period.

Since the outbreak, Bitcoin is up by 131%, Ethereum by 193% and Gold futures by 44%. The return from these assets more than compensated for their increased downside risk and cross-asset correlations.

Crypto allocation – Case B – We checked whether allocations made according to a mathematical optimization could have generated a better result over the rule of thumb. The optimization was run on the pre-covid data set with the objective of maximising the Sortino ratio. These weights were then applied to the post-covid dataset.

The optimization result is a 51-49% split between the risky assets and safe havens. Amongst the risky assets, the max allocation is 32% to S&P 500 while the least is 0% to Ethereum, which had the highest downside volatility. The total crypto allocation was only 5% in Bitcoin. Amongst the safe assets, the entire amount was allocated to Gold futures.

The optimization failed to produce a superior Sortino ratio in the post crisis period as compared to the 60-40 case. The reduced allocation to crypto missed out on the rally in both the cryptos, especially Ethereum in its entirety, leading to an erosion of the portfolio value. Clearly, the optimization weights were not optimal for a period of market stress.

Interestingly, the portfolio risk increased by 3.7x – almost double than in the 60:40 case – while the return was half than in the 60:40 case during the outbreak. The Sortino ratio fell to 1.66 post crisis from 4.62 pre crisis; this is much lower than that in the 60:40 case – a ratio of 1.95 pre-covid and 2.18 post-covid.


Past returns may not repeat themselves. However, it is worth giving some thought to holding cryptocurrencies as part of an investment portfolio. During periods of market stress, their downside volatility and correlation with the broader market may increase, however, the diversification benefit could help preserve portfolio value and the increased risk may be offset by higher returns. Intra-crypto diversification could also be explored for further risk management.

We found that a 30% allocation to cryptos significantly aided portfolio performance during the crisis, up until now. This allocation could be adjusted upward or downward based on an investor’s risk appetite, however, if it is kept too low, the diversification benefit is lost. If kept too high, it would increase portfolio risk.

The same research could be replicated for other stressed periods in the past and updated with future data, to test the robustness and validity of these findings. For making an informed market entry, we recommend that this research be complemented with the study of crypto asset valuation and/or price action over a longer time horizon.


¹A safe haven, as the name implies, is an investment which retains or increases its value during times of market turbulence.

²The Sortino ratio is a measure of risk adjusted return where the risk is only downside volatility; the Sharpe ratio considers both – upside and downside volatility.

³This is a mathematical optimisation procedure, also referred to as the mean variance framework; it iteratively finds the optimal portfolio allocations given the data inputs of individual asset returns, volatilities and cross-asset correlations and an optimisation objective such as maximise portfolio return or minimise portfolio risk.

⁴The correlation coefficient measures the extent to which two assets move together. The value can range between -1 and 1 with 1 indicating perfect positive correlation and -1, a perfect negative correlation.

Concept Explainers

Cointegration Demystified

The tale of a drunk and her dog

In 1987, two Nobel prize-winning economists introduced the concept of a co-integrating vector through their research paper (Engle & Granger)¹.  (Murray, 1994)² illustrated the concept of cointegration through the now famous tale of “A drunk and her dog”.

A time series is a series of data points ordered in time. For example, the price of a stock over the past 5 years. Two time series may behave like two drunk people wandering around. The two people are independent; there is no meaningful relationship between their paths. Knowing where one of them is, may not help us find the other drunkard. However, given a drunkard’s location, it could be possible to predict, at least to some extent, where her dog might be. Let’s call him Coco. The path followed by both is still unpredictable. However, given the location of one, we might be able to predict the location of the other. In other words, the distance between the two is fairly predictable.

The drunk owner and her dog Coco form a cointegrating pair. Note the probabilistic nature of the cointegration. Coco is not on a leash; the distance between the drunk and the dog is not fixed. However, it is likely that if they end up too far apart, Coco will run back towards his owner, reducing the distance between them to what it usually tends to be.


Simple definition:
Cointegration is a statistical property exhibited by time series data. The movement of two time series together is called cointegration. It refers to a long-run equilibrium relationship between the two time series.

Technical definition :
Mathematically, two time series, say X and Y, are cointegrated if both of them, individually, are integrated of order d [I(d)] but there exists some combination of them, such as, aX + bY, which is integrated of order zero [I(0)].³

Cointegration can be tested for using the Engle Granger and Johanson cointegration tests.

Application in trading strategies

We can extend this concept to financial assets – cointegrated stocks, futures, currencies and more. If the stocks Amazon and Alphabet are cointegrated, there is some relationship between them that could allow us to predict how they are likely to move, in relation to each other. If their ratio tends to remain constant in the long run, long short trading strategies can be built around exploiting the short run deviations from the average ratio. This can be explained in greater detail later;  the concept of pairs trading and statistical arbitrage deserves a separate article.

Cointegration vs correlation

These are two separate concepts.
1. Cointegration is the co-movement and mutual association of two time series through some combination of them; correlation refers to the directional relationship between the two time series. Neither necessarily implies causation.

2. Correlation is a short-run concept while cointegration is a long-run concept. Correlations are more unstable and sensitive to the length of the period over which they are calculated.

3. It is possible for a cointegrated pair to be uncorrelated and for a correlated pair to not exhibit any cointegration. For example, two positively correlated stocks may grow further apart in the long run even if they move in the same direction in the short run and vice versa.

The absence of correlation does not indicate independence of two time series.

4. Because of the nature of most of the financial time series data (nonstationary⁴), the correlations between them may be spurious (false). Cointegration is a stronger, more reliable measure. For example, two time series could appear highly correlated simply because both are trending higher over time; they may have no actual relationship. Not only does this lead to absurd results, these results also appear to be falsely statistically significant; the usual T and F statistical tests are not applicable for non-stationary data; they assume stationarity (constant mean, autocovariance).

Example of a spurious corrrelation: The US Defense Expenditure and the population of South Africa has a correlation of 0.97 over the period 1971-1990.⁵

Two time series are cointegrated only if there is a genuine relationship between them. It is possible to create trading strategies based on correlation as well. However, one would be well advised to do a sense check; how meaningful is that relationship and the chosen time horizon?


¹Engle, R. F., & Granger, C. J. (1987, March). Co-Integration and Error Correction: Representation, Estimation and Testing. Econometrica, 55(2), 251-276.

²Murray, M. P. (1994, February). A Drunk and Her Dog: An Illustration of Cointegration and Error Correction. The American Statistician, 48(1), 37-39.

³This is the order of integration concept. An I[1] series needs to be differenced once for making it stationary i.e. I[0].

⁴A non-stationary time series is a time series which does not have a constant mean and autocovariance over time, rendering it useless for prediction, unless transformed into a stationary series.

⁵Examples of spurious regressions:

Concept Explainers

FX Carry Trading Part 2

In Part 1 of this series we covered the lingo and mechanics of a carry trade. Thank you for your feedback for Part 1! Part 2 focuses on the importance, risk and return of this strategy. As suggested by our readers, we also explain the concept of hedging. Let us carry on!

Why do we care about carry trading?

We chose to write on this topic because it illustrates a modern application of financial engineering in practice.

Japan has faced zero, near zero or negative interest rates for close to three decades now.

In the current macroeconomic environment, interest rates in developed economies are either very low or negative. Carry trades could serve as an investment product offering superior returns, useful for medium and long term investors. Carry trades tend to attract hot money, invested by those that actively seek out returns in the short run. But they could also prove useful for large institutional investors such as insurance companies (mainly life insurance companies), pension funds and endowment funds which generally seek long term investment opportunities and hold bond positions till maturity.

When is a carry trade profitable?

This is when the extra coupon exceeds the loss (if any) on an adverse exchange rate movement. We would hope for either the currency pair to remain stable over the holding period or move in our favour (for extra return from the target currency appreciation).

What are the risks involved?

  1. Exchange rate risk. Foreign (target currency) depreciation or devaluation by Central Banks inflicts losses. Emerging market currencies tend to be very volatile.
  2. Interest rate risk: Monetary policy decisions by Central Banks (changes in interest rates and outlook).
  3. Negative market sentiment and heightened volatility. Uncertainty and fear can lead to carry trade unwinds. This can cause large exchange rate movements, inflicting further losses.
  4. Leverage (if any) will magnify losses.

What is an example of a real-life carry trade?

Julian Robertson, a billionaire hedge fund manager, is one of the most famous carry traders in history. He used to trade USD/JPY on leverage. In the period between 1995 and 1998, USDJPY appreciated by more than 66% (caused partially due to carry traders who bought the dollar and sold the yen). The carry was 15% at the time. So his total return was around 81% p.a. However, in 1998, due to the Russian debt crisis and the near collapse of LTCM, carry trades were unwound and this caused a sudden appreciation of the yen. Robertson is said to have made huge losses, of around $2 billion¹.

Why are carry trades unhedged?

Hedging means reducing the risk of a transaction. In part 1, we illustrated a USDTRY carry trade. The depreciation of TRY is the foreign exchange risk in this transaction. This would mean that the Turkish Lira has become less valuable. Hence, on conversion we would get less USD. One way to reduce this risk (hedge) is to buy a forward on USDTRY.

A forward is an instrument which allows you to fix the rate at which you would do the conversion in the future. If you go long (buy) a forward on USDTRY, on a fixed date in the future, you will sell your TRY holdings to buy USD at a fixed rate which is known to you now itself.

Carry trades are usually unhedged; no forward is purchased to reduce the risk. This is because sometimes carry trades are entered into mainly for exposure to the FX risk. An investor may have a view that the target currency TRY will appreciate or USDTRY will remain stable over the investment period. The potential return from undertaking the FX risk could largely outweigh the carry.

What makes a carry trade possible?

According to interest rate parity theory, it should not be possible to make a return because the higher yield currency should depreciate by the extent to which the yield is higher. However, it was been observed that this theory does not always hold. This anomaly is called the Forward Premium Puzzle. Empirical findings indicate that sometimes the currency with the higher interest rate appreciates instead of depreciating, which makes carry trades possible.

Can the concept of carry be applied elsewhere?

“Carry” simply means the return that you make by holding an asset or a position. This concept can be applied across asset classes.

Types of carry trades:

  1. Currency/bond carry trade (Using spot or derivatives or bonds to take positions)
  2. Yield curve carry trade (Trading different maturities)
  3. Commodity carry trade (Roll yield)
  4. Equity carry trade (Long short dividend yield)
  5. Credit carry trade (Long short credit spread)


¹Robertson’s carry trade profits -

Concept Explainers

FX Carry Trading Part 1

In part 1 of this series, we cover the meaning and mechanics of a carry trade. In part 2 (upcoming next week), we will cover carry trading significance, risks and return in more detail.

Technical definition (Ours): A carry trade is an unhedged investment in another currency due to the higher absolute yield at the time of the investment.

What is a carry trading strategy?

Simple meaning: Borrow money cheap and invest it where you get high returns.

Below is an illustration of a carry trade using bonds.

Example: As of writing, the 1 year US Government bond yield is around 0.2% and the 1 year Turkey Government bond yield is much higher at around 8.4%. Short (sell/borrow) the US Government bond and go long (buy/invest) the TRY Bond. This would result in a return of 8.2% if the USDTRY exchange rate remains unchanged. If TRY depreciates, this return will reduce (on conversion you will get less USD).

This is interest rate arbitrage. We define arbitrage here as “the simultaneous purchase and sale of the same or similar security in two different markets for advantageously different prices” (Sharpe and Alexander, 1990)¹. However, this does not satisfy the other usual definition of arbitrage, which refers to risk free profit. Because the foreign exchange risk is not hedged, the transaction is NOT risk free.

What are the components of a carry trade?

Funding currency (Home currency) – The currency in which the lower interest-paying bond is denominated. Popular funding currrencies: YEN, CHF, EUR.

Target currency – The currency in which the higher interest-paying bond is denominated.
Popular target currencies: TRY, RUB, INO, CNY, INR.

The funding currency is used to buy the bond denominated in target currency.

Carry – The difference in the interest rate of two government bonds in different currencies. This is the incentive for the trade.

FX Return – The target currency appreciation would provide an additional return over and above the carry.

That’s it for this article. Let us know your thoughts in the comments below!

Reference: ¹ Sharp, W. & Alexander, G. (1990). Investments, 4th edition, Prentice Hall, Eangle-Wood Cliffs, N. J.

Concept Explainers

Dynamic Trading Strategies

Fixed trading strategies cannot adapt to the market. You could wear the same tee shirt everyday but at some point you will sweat and that shirt is going to smell. That’s stale, boring and risky. You should probably adapt your clothes washing routine to the weather.

Dynamic trading, as the name suggests, is trading using strategies which quickly adapt to such changes. This may mean, including new, more recent data in your analysis for your trades. This could also involve changing your strategy or adjusting its parameters as seems appropriate. You could change your shirt AND shine your shoes too.

Example – Assume that my love for Elon Musk, his future plans for Tesla Inc and my financial analysis has made me bullish on the Tesla stock for the coming few weeks. The stock has been swinging quite wildly and this volatility is expected to continue.

Buy Tesla at the start of the trading session every morning and sell it when it reaches a high.

But how do I set my profit target and stop loss? Let us say I check the range in which stock has remained for the past week. A 5 day average tells me that the stock moved by 150 points intraday (High – Low). I shall set my profit target 150 points above the share price at the start of the session and my stop loss 150 points below. So if the price at the start of the session is 900, my target will be 1050 and stop loss will be 750.

Adaptive component:
The extent of volatility is likely to change over the coming days. What change can I make to try and maximise my winnings? I can make the trading range dynamic. The 5 day average will be updated to include the latest trading session and exclude the oldest one. The average will therefore, move with the market and my profit target and stop loss levels too.

Other examples of adaptive components:
– Dynamic technical indicators (7 day moving average vs 20 day moving average)
– Rolling statistics such as correlations (say, 20 day moving average since relationships between two securities can change over time)
– Trade amount (1% of my account balance. If I’m making more money, I can afford to place bigger bets!)

A related term is Dynamic Hedging (more popular). It’s the same concept, used in risk management, where you actively adjust the hedge for a position.

Concept Explainers

Big Data

What is big data?

Technical definition: Big Data refers to datasets whose size is beyond the ability of typical database software tools to capture, store, manage and analyze.*

Simple definition: Big Data is a buzzword for large amounts of data.

The Vs of Big Data:
1. Volume (High Quantity)
2. Velocity (High speed of capture)
3. Variety (High complexity)
4. Veracity (Trustworthiness)
5. Value (Meaningful)
6. Visualisation (Graphical representation)

Uses for Big Data in Finance:
-Financial modelling
-Real time analytics
-Algorithmic trading
-Machine learning

Example of big data being used in trading:
A Hedge Fund called Coniecto Technologies uses Big Data to estimate its investment risks. For this it gathers a lot of data to make more precise estimates.

1. Volume – Past data of market variables (stock indices, FX, Bonds, Commodities, Crypto price and volumes) since inception
2. Velocity – Hourly crypto price and volume data
3. Variety – Analyst reports, news feeds, sentiment analysis of Twitter
4. Veracity – Official data from trustworthy exchanges
5. Value – Helps to understand relationships between market variables, say, exchange rates and interest rates
6. Visualisation – Heat map indicating volatility of assets (Colours low to high volatility using a green to red gradient)

Challenges in using Big Data:
1. Access to data (Could be expensive or out of reach)
2. Inconsistent and incomplete data (For example – Missing values)
3. Heterogeneity of data (Diversity) (prices, reports, social media analytics etc)
4. Data privacy and protection (ethical considerations)

Some Big Data tools:
Apache Hadoop


Concept Explainers

Quantitative Trading

Quantitative trading means trading (buying and selling securities such as stocks) using certain specific strategies. We use math and Big Data (large amounts of data) to discover patterns in their movement. The trading is sometimes automated (run by a computer without humans).

A very simple example : Buy Tesla shares today if the stock has risen continuously for the past 3 days. We can calculate how likely it is that this strategy might work. For the past 2 years, how many times did the stock rise on the 4th day after a continuous rise for 3 days?

Quantitative trading involves the below steps:
1. Gather Data
2. Backtest strategy (Check if a strategy could have worked in the past)
3. Strategy Execution (Trade using real money)
4. Manage risk (Try to limit your losses)

Quantitative Trading includes:
    – Low Frequency Trading
    – High Frequency Trading
    – Statistical Arbitrage
    – Algorithmic Trading