Risks and returns are two sides of the same coin. Higher returns entail higher risks and that is why it is essential to understand both the facets of risk in detail. Let us look at types of risk and returns and look at risk-return trade off. Let us also look at risk and returns with specific respect to mutual fund investments to get a better perspective.

Understanding the Risk-Return Trade-Off

Every mutual fund investment decision is a risk-return trade off. Basic finance teaches us that higher returns are associated with higher level of risk. Thus higher the level of risk that you undertake the higher is the return that is expected by you. If you go lower down the risk scale, then there are lower returns in the offing. Let us understand the steps to grading risk and returns when it comes to mutual funds.

RISK REWARD RATIO

The 4 steps to risk-return trade-off in mutual funds are as under:

Step 1: At the lowest end of the spectrum are the liquid funds. These funds typically invest in very liquid asset classes like call money, government treasury bills, certificates of deposit, commercial paper etc. These are virtually risk free and since they are short term instruments, they are less vulnerable to movements in the interest rates. The products they invest in are government backed instruments where the default risk is almost nothing.

Step 2: At the second level are the debt funds. Debt funds become risky for two reasons. Firstly, they are long term funds. They invest in long dated government securities. While these government securities are still free of default risk, they are prone to interest risk. In fact, longer the maturity greater is the vulnerability to shifts in interest rates. Secondly, debt funds invest in a mix of government securities and corporate debt. These corporate debt instruments do run a major price risk as we saw in the case of Amtek Auto.

Step 3: At the third level are the hybrid funds. A classic example of a hybrid fund is a balanced fund. Balanced funds invest in a mix of equity and debt instruments. As a result, the returns on these funds are slightly higher than debt funds but lower than pure equity funds. The major attraction of balanced funds is that despite a 35% exposure to debt, they are classified as equity funds for the purpose of calculating tax on capital gains. That makes them more attractive in post-tax terms.

Step 4: At the highest level are the equity funds which are predominantly invested in equities. Of course, equity funds do try to reduce your overall risk by diversifying across asset classes and sectoral exposures. But equity, being an instrument that does not offer assured returns, is more risky than debt. Even within the gamut of equity funds, the sector funds and thematic funds tend to be more risky as they are more vulnerable to specific risks and do not bring the benefit of diversification.

Understanding Concentration Risk

There are broadly 4 types of concentration risk that you could be exposed to…

Risk of concentration in a sector – which broadly refers to over exposure to a particular sector like banking / pharma which elevates the downside risk of cycles.
Risk of concentration in a theme – which is about overexposure to a theme like rate sensitivity, commodities etc which represent a set of sectors with similar triggers.
Risk of concentrated exposure to macro triggers arises from vulnerability to inflation, liquidity tightness, commodity prices, Chinese demand etc.
Concentration risk in debt portfolio arises when the debt portfolio is tilted in favour of long duration, long maturities, credit risk etc.

Risk Involved In Debt Market Investments

Contrary to popular belief, debt is not risk free. Even G-Secs are only free from default risk, but is still exposed to other risks. Here are some key debt risks.

Inflation risk in bonds

We all know that inflation is a measure of rise in prices. Inflation is a key macro measure because it measures the reduction in the value of your money. For example if the inflation rate is 10% then Rs.100 today is worth just Rs.90 after 1 year and worth Rs.81 after 2 years. Your money is getting eroded even without your doing anything as the rise in the general price level is eroding your purchasing power. Why is it a risk for government bonds? Let us assume that you are earning 8% on a government bond and the inflation rate is 5%. That means net of inflation you are earning a real return of 3% on the bond. What if inflation goes up to 9% due to a surge in food prices following a bad monsoon? Then your real return is actually (-1%).

Interest rate risk in government bonds

We are aware that there is a negative relationship between interest rates and bond prices. When rates go up bond prices come down and when rates go down then bond prices go up. That is why bond funds tend to outperform the market when rates are headed downward. But what if rates start increasing? Then the bond prices will start falling and if you are invested in government bond funds then your NAV will start to depreciate. This is called price risk or interest rate risk. In fact, this risk is more pronounced in case of government bonds because these are mostly liquid and long-dated and hence more vulnerable to the price risk.

Reinvestment risk in government bonds

This is a slightly more complex argument pertaining to the risk of investing in government bonds. When you invest in government bonds then you get interest at periodic intervals and then you get back the face value of the bond at the time of maturity. That is fine but then let us come to the concept of yield to maturity (YTM). When the market quotes the YTM of the bond at 7.5%, there is an implicit assumption in it. The assumption is that your interest receipts are actually reinvested at the same YTM. But if you use up the interest for other purposes then the actual yield on the bond will be lower than the YTM that is claimed.

Risk of not taking on sufficient risk

This is popularly called the hidden risk of investing in government bonds. If you earning (-1%) real returns on your bonds then you are actually destroying wealth over the long run. You would be better off taking a higher degree of risk in equities and facilitating the creation of wealth in the long run. Here, the biggest risk is not taking on enough risk.

Key Risks of Thematic / Sectoral Funds

Let us first understand the key risks of investing in thematic funds in the Indian context…

Thematic funds concentrate portfolio risk

Thematic funds are less concentrated compared to sector funds but are still more concentrated compared to diversified equity funds. The concentration risk can arise in thematic funds for a different reason altogether. Take the case of the rural consumption story back in mid-2016. The setting was absolutely perfect with a bumper agricultural crop and the government committing higher funds to the farm sector. Had you invested in a rural consumption theme fund at that point of time, you would have been in for a shock in November when the government announced the demonetization drive. It created a sharp liquidity crunch in rural areas and these rural consumption stocks were the worst hit. Your theme would have really disappointed you in the first half of 2017.

You may overexpose your portfolio to negative triggers

While sector funds have sectorial triggers, thematic funds tend to have thematic triggers. The impact of demonetization on the rural theme story is a case in point. Take the case of infrastructure as a theme. Higher government investment in infrastructure is a big boost for this theme. But the huge exposure of banks to infrastructure NPAs is an overhang. Any decision by the banks to get tough on these NPAs could have negative repercussions on this theme which you need to be prepared for. You may believe that you are better off than in case of a sectoral fund but actually your vulnerability to negative triggers could be quite high.

Global factors can be a major threat for the fructification of thematic funds

When you understand triggers pertaining to thematic funds, the triggers can come from a variety of sources. Take the case of the unwinding of the technology theme in 1999 and the unwinding of the infrastructure theme in 2008. In both the cases, the actual trigger for the end of the theme play came from abroad. That is the big risk as you do not have any control or any warning signals. Any thematic fund entails tracking a plethora of domestic and international triggers that could bring the theme into danger. That is the big challenge.

Understanding Risk and Uncertainty

Risk can be understood as the potential for loss. Here loss is defined a little more broadly. It is the probability of a bad thing happening or a good thing not happening. For example, if the profits of a company fall in one quarter, that is a business risk for the company. Similarly, if the market is expecting a 20% growth in profits and the profits actually grow by only 10%; that is also a risk. Risk is a bad event happening or a good event not happening. In financial markets, risk is measured by the volatility of returns.

What exactly is uncertainty?

If uncertainty also looks like risk, it is actually different. As the name suggests, uncertainty is the absence of certainty. Since the event itself is uncertain, the outcomes also become uncertain. Since the outcomes are uncertain, it becomes difficult to define uncertainty or to measure it. Uncertainty, therefore, reflects a situation where you are not sure of the outcomes. For example, we all know that scientifically Maharashtra is earthquake prone. But it is uncertain whether the earthquake will hit the region in the next 3 years or 5 years. Since the event itself is uncertain, despite being possible, it is hard to measure the outcomes.

Differences between risk and uncertainty

The key difference between risk and uncertainty is best captured by this statement that “Risk is measurable uncertainty while uncertainty is immeasurable risk”.

Uncertainty denotes a situation where the future events are largely unknown. Since the events are unknown, the outcomes are also unknown. Since the outcomes are unknown, it is hard to assign probabilities to the possibility of occurrence. Effectively, this makes it hard to measure and assign a probability to. Risk, on the other hand, refers to a future event which can be known with reasonable degree of certainty. While the actual event is still unknown, you can assign probabilities to the occurrence of various possibilities based on past experience. That is what makes risk measurable and also manageable.

RISK AND UNCERTAINTY

The chart above is fairly illustrative of the differences between risk and uncertainty. It best captures the relationship between risk and uncertainty. For example, when the probability of occurrence of an event is certain, then the possibility of failure is low and the managerial control is very high. When the event is uncertain, then the possibility of failure is very high while the managerial control over the event is very low. Managers, for example, have a very low control over a Tsunami hitting their factory near the coast, which normally happens once in 150 years. Risk is in between these two extremes. The beauty of risk is that while there is still uncertainty over the occurrence of an event, these are based on known factors. Therefore, probabilities can be assigned and managerial decisions taken accordingly.
From a business point of view, risk can be controlled. Let us take the case of a portfolio with systematic and unsystematic risk. The unsystematic risk can be managed by diversifying away from stocks and sectors that are going through trouble. Similarly, the systematic risk can be reduced or managed through beta hedging against Nifty futures. But from a business point of view, uncertainty cannot be measured and therefore cannot be managed.
Remember, since you cannot manage or control uncertainty, you normally take insurance against it. That is where the role of insurance comes into uncertainty. There is no insurance against risk but there is insurance against uncertainty!

Why the risk-return trade-off is important to an investor?

There are 6 essential reasons why the risk-return trade-off has immense practical application.

It helps you to understand the risk-return relationship. This forms the basis of your portfolio creation and long term planning towards your financial goals. If you have a longer time frame you need to earn higher returns and therefore you can afford to take on higher risk. That means; you can reach your goals with a smaller monthly SIP outlay.
It is very important to grasp the causality of the relationship. For example, higher returns entails higher risk but higher risk does not necessarily mean higher returns. For example, you can take a very high risk by putting all your money in a commodity fund. But if the commodity goes through a prolonged multi-year bear cycle then your portfolio will grossly underperform and give negative returns although you have taken on higher risk. Hence you should only take on calibrated and measured risk.
Creating a risk-return matrix lies at the core of financial planning. One of the best ways to do it is to bucket asset classes into various risk-return buckets and then select the asset class that corresponds closest to your financial goals. For example, liquid funds for 1 year goals, Short term funds for 2 year goals, debt funds for 3 years goals, debt funds for 5 year goals, balanced funds for 7 year goals, Equity funds for goals above 10 years etc. This matrix simplifies your job of financial planning and asset allocation.
The risk-return trade-off helps you to quantify the units of risk you are willing to take for every unit of return. Let us understand this from the point of view of trading. Your risk-return acceptability is 3:1. That means if your stop loss is 1% lower than your profit target must be 3% higher. Extrapolate this concept to your financial investments and you have a quantifiable risk-return matrix in your hand.
It helps in portfolio optimization. What do we understand by portfolio optimization? For a given level of return you need to minimize the risk or for a given level of risk you need to maximize your returns. Once you have the total risk that you are willing to take, you can break it up into sub components for each asset class.
Remember, portfolio creation is not just about aggregating assets but also about understanding their internal correlations. Lower the correlation of assets in a portfolio, the lower is the risk due to internal risk set-offs. When you have laid out the risk-return matrix and know that risk needs to be reduced in tune with returns, you have a choice of diversification. That is the luxury that risk-return trade-off accords to you.

Different Approaches to Measuring Returns

When we talk of returns, it is a nuanced subject and has many implications. Let us look at some popular types of return calculations.

Arithmetic mean of investment returns

This is the simplest way of calculating returns on an investment. Let us consider the case of an investment where we invested Rs.10,000 in a stock and then evaluate the price after 5 years. Here is how it looks…

Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
10,000	11,500	16,000	17,200	15,500	18,900
Profits / Loss	1,500	4,500	1,200	-1,700	3,400
Returns (%)	15.00%	39.13%	7.50%	-9.88%	21.94%
Arithmetic Mean Returns =	14.74%	(73.69 / 5)

What the above table indicates that the return on the investment over a 5 year period was 14.74%. The only problem with using an arithmetic measure is that this mean is very vulnerable to large numbers. The massive profit earned in Year 2 has sharply distorted the returns into positive territory.

Compounded Annual Growth Rate (CAGR)

The second approach to calculating returns on your investment is the CAGR of returns. Here we assume that when you hold the asset for a period of 5 years then the returns made each year does not matter. Instead, what matters is what returns were generated over a period of 5 years and how that translated into an annualized IRR. In the above case, Rs.10,000 invested at the beginning of year 1 grew to Rs.18,900 at the end of year 5. What does that translate into in terms of annualized compounded returns? We can use the standard compounding formula in this case as under:

Corpus at year 5 = Investment at Year 0 X (1 + R)⁵

In the above case we need to find the missing compounding rate of “R”, which will be the 5^th root of the wealth ratio i.e. (1.89)^1/5 = (1 + R). Thus R = 13.58%

The above formula works very well for long period returns when the asset price is moving in a secular trend. When the trend is volatile and unpredictable then CAGR does not give clear results.

Geometric returns when there are intermittent losses

The arithmetic measure of returns can be misleading in the case of losses. However, there is an alternate method called the Geometric returns. This tends to smoothen out the positive and negative returns by converting them into relative numbers. Here is how it works…

Details	Year 1	Year 2	Year 3	Year 4	Year 5
Year Returns	12%	-8%	15%	-3%	21%
Factor of 1	1.12	0.92	1.15	0.97	1.21

Geometric Mean = {(1.12*0.92*1.15*0.97*1.21)^1/5} - 1

Geometric Returns = 6.82%

The big advantage of the geometric mean approach is that it smoothens out the vagaries of the stock over a longer period. Under normal growth it gives the same rate of return as the CAGR returns and close to what the Arithmetic mean gives.

Return on average sum invested

This is a very useful measure of returns when your principal invested keeps changing. Here the returns are not being seen in terms of price movement on a year on year basis but the profits earned by you net of costs is measured against your corpus. But what is your corpus since it keeps shifting through the year. That is why the average corpus is used.

Details	Capital on Jan-01	Capital on Jan-30	Gross Returns	Net Returns
	Rs.100,000	Rs.150,000	Rs.31,000	Rs.25.400
Average Capital	Rs.1,25,000
Return on Average Sum Invested	20.32%	25,400/1,25,000

Return on average sum invested is more relevant when we are taking a portfolio approach and therefore the net returns are of greater importance.

Dollar adjusted return on investment

The dollar adjusted returns may not be too relevant to Indian investors. But this matters to international investors like NRIs, foreign portfolio investors etc who need to measure their returns in dollar terms. Therefore, apart from the domestic rupee returns, the movement of the dollar also matters. Let us take the case of 2 investors who invested the same amount and earned the same returns but at different points of time. While Investor A faced a strong dollar, Investor B faced a weak dollar.

	Investor A		Investor B
Basic Investment	Rs.1,00,00,000	Basic Investment	Rs.100,000
Rupee / Dollar	65/$	Rupee / Dollar	65/$
Dollars Paid	$153,846	Dollars	$153,846
Value after 1 Yr	Rs.1,25,00,000	Value after 1 Yr	Rs.1,25,00,000
Rupee / Dollar	68/$	Rupee / Dollar	63/$
Dollars Received	$183,824	Dollars Received	$198,413
Rupee Returns	25%	Rupee Returns	25%
Dollar Returns	19.49%	Dollar Returns	28.97%

As can be seen in the above instance, Investor B has benefited by the dollar depreciation which has actually enhanced his rupee return by 3.97%. On the other hand Investor A has lost (-5.51%) due to the impact of the dollar appreciation. The dollar movement makes a big difference to international investors.

Nominal, Real and Post Tax Returns

Nominal return versus real return is a fairly straightforward point. You earn returns when you invest in stocks and bonds. But then inflation takes away a part of the return in the form of higher prices. In economics, Inflation is regarded as the biggest thief of value. When you look at nominal returns adjusted for inflation then you get real returns. Let us understand this concept of real returns a little better with a formula to calculate inflation adjusted returns…

Variable	Current Value	After 1 year	After 2 years
Interest rate on Bond		10%	10%
Inflation		6%	6%
Investment value	Rs.1000	Rs.1100	Rs.1210
Nominal Returns		Rs.100	Rs.110
Inflation adjusted PV 1-year & 2-years		Rs. 1038	Rs.1142
Real Profit (Net of Inflation adjustment)		Rs.38	Rs.42
Real Return (%)		3.80%	3.82%

In the above example to calculate inflation adjusted returns, we can see that the real returns are substantially lower than the nominal returns due to inflation.

Pre-Tax returns versus post tax returns

Another way to look at returns is in the form of pre-tax returns versus post tax returns. The tax adjusted returns formula will differ according to situations viz. tax rebate on investments and tax on income flows.

Situation 1:

How do you compare the returns on an ELSS fund with a normal equity mutual fund? Structurally, both the funds are the same except that an ELSS fund has a 3-year lock in and therefore offers a tax rebate on the investment. How does that impact returns?

Equity Fund	Particulars	ELSS Fund	Particulars
Fund name	Alpha Equity Fund	Fund Name	Alpha Tax Saver
NAV on 01-12-2014	Rs.20	NAV on 01-12-2014	Rs.20
NAV on 30-11-2017	Rs.35	NAV on 30-11-2017	Rs.35
Absolute Returns (%)	75%	Absolute Returns (%)	75%
CAGR Returns	20.5%	CAGR Returns	20.5%
Section 80C Rebate	Nil	Section 80C Rebate	30%
Effective Investment	Rs.20	Effective Investment	Rs.14 (20-6)
Effective Returns (%)	75%	Absolute Returns (%)	150% (21/14)
Effective CAGR (%)	20.5%	CAGR Returns	35.8%

In the above case, look at how the effective returns increases substantially in case of Alpha Tax Saver due to the Section 80C benefit. The actual benefit will depend on the tax bracket.

Situation 2:

How does the impact on taxation change the effective comparison of different bonds with different rates of returns? Let us consider the example of a Corporate Bond and a NHAI tax-saving bond. The table shows the comparison…

Corporate Bond	Particulars	Tax-Free NHAI Bond	Particulars
Face Value of Bond	Rs.1000	Face Value of Bond	Rs.1000
Annual Coupon (%)	9%	Annual Coupon (%)	7%
Tax status	Fully Taxable	Tax Status	Tax Free
Pre Tax Interest	Rs.90	Pre Tax Interest	Rs.70
Post Tax Interest	Rs.63 (90-30%)	Post Tax Interest	Rs.70

In the above case, the corporate bond pays a 200 bps higher coupon compared to the tax-free bond. However, when you consider the tax impact of 30% on the corporate bond, the tax-free bond actually works out to be more attractive.

Absolute Returns Versus Total Returns

Absolute returns are nothing but the point to point returns. So if the price of the stock on 1^st Jan 2017 was Rs.200 and the price was Rs.240 on 31^st Dec 2017 then the 1 year absolute return will be

20% = {(240-200)/200} x 100.

Absolute returns purely consider the price movement from one point to another. We can use absolute returns for calculating 3 months returns, 6 months returns, 1 year returns, 3 year returns or 5 year returns. In case of tenure longer than 1 year, it is advisable to use the CAGR (compounded annual growth rate) to get a clearer picture.

Total returns consider the impact of dividends. Let us go back to the previous example and let us assume that the company also declared a dividend of Rs.5 during the year. Total returns will consider these dividends too. So the Total returns on the stock now will be as under…

22.50% = {(240+5-200)/200} x 100

As we can see, the total returns on the stock are higher because the dividends are also considered whereas in the first case the dividends were not considered. But why is this distinction so critical for measuring the performance of mutual funds…

Why is the Total Return a better measure for mutual funds than absolute returns?

Before we get into the technicalities of the calculations for Total Returns and Absolute returns let us first understand how an equity mutual fund functions. A mutual fund holds shares on behalf of its unit holders. Any dividends declared by the company accrue to the mutual fund. Secondly, any profits booked by the mutual fund on sale of shares also accrue to the mutual fund. Lastly, when stocks appreciate, the notional profits also contribute to the NAV of the fund. So when we calculate the returns on a mutual fund as the point-to-point NAV then we consider the dividends received, the profits booked and the notional profits that have not been booked.

We now come to the question of benchmarking the mutual fund performance against the index. That is where the dichotomy arises when you consider absolute returns. The absolute point-to-point returns of an equity mutual fund consider dividends and price appreciation. But in case of indices like Nifty and Sensex, the point-to-point returns only capture the price movement and not the dividends received by the index stocks. This could result in a situation where the returns of the index tend to get understated. That means the equity fund’s outperformance vis-à-vis the index tends to get overstated to the extent of the dividend yield on the index. Total Returns Index overcomes the problem by adding up the dividend yield to the index returns to give a more reliable picture.

TRIs can reduce the outperformance claimed by equity funds…

As mutual funds shift from ARI to TRI for benchmarking mutual fund performance, the investors will get a clearer picture. Let us understand how the shift from ARI to TRI will make a difference to the way fund performance is measured…

Fund and Index (ARI)	Amount and Returns	Fund and Index (TRI)	Amount and Returns
NAV of Fund X - Jan 01	Rs.20	NAV of Fund X - Jan 01	Rs.20
NAV of Fund X - Dec 31	Rs.26	NAV of Fund X - Dec 31	Rs.26
ARI for Fund X	30%	TRI for Fund X	30%

Nifty Value – Jan 01	10,000	Nifty Value – Jan 01	10,000
Nifty Value – Dec 31	12,700	Nifty Value – Dec 31	12,700
ARI for Nifty	27%	ARI for Nifty	27%

		Dividend Yield on Nifty	2%
		TRI for Nifty	29% (27% + 2%)

ARI outperformance	3% (30% - 27%)	TRI Outperformance	1% (30% - 29%)

When one looks at the above tabular comparison, the importance of the TRI over the ARI becomes much more obvious. In case of the fund, the equity fund receives the dividends and the capital gains and hence the change in the NAV reflects the ARI and the TRI for the equity fund X. In case of the Nifty index, the TRI is 29% as against the ARI of 27% when the 2% dividend yield on the index is considered. Mutual Fund investors will get a clearer picture of the performance and that is the key takeaway!

Module V

CHAPTER 3 - Managing Investment Risk and Measuring Investment Returns