# Should I borrow to invest? And how much leverage can I take on?

Should I borrow to invest? In our earlier post * How to Invest with Leverage Safely*, we discussed how an investor can now have easy access to credit for investment, and how this borrowing can be used to increase returns. Of course, at its most basic, borrowing to invest can increase returns, but at the cost of increasing risk. Hence, from a risk-returns point of view, there is nothing superior about borrowing to invest, over investing on a fully cash basis. You get more returns, but take on more risk.

But in the same post, we also investigated the case where borrowing is done to invest in a low risk bond fund, with leverage being applied to bring the expected return to the same level as a equities portfolio. Subsequently, the combination of both the leveraged bond portfolio and the unleveraged equities portfolio is done to increase the returns on the overall portfolio to a level of a 100% equities portfolio, but with only the risk of a 60:40 equity-bond portfolio. Borrowing is done not just to increase returns, but to lower risk as well!

So, should I borrow to invest? It does seem quite evident that there is a good case to be made for borrowing to invest. And this is not for increasing returns, but rather, for decreasing risk, and so doing, improving the risk-return tradeoff beyond what a simple stock-bond portfolio can offer. We will explore this more nuanced approach to investment portfolio management in the following section. Also, we will go into a bit more detail as to the other question: How much leverage should I take on to invest?

#### Should I borrow to invest?

Let’s start with the first question of “Should I borrow to invest?”.

When most of us approach borrowing for investments for the first time, it is typically during an early stage in our investment journey when we are still fairly unsophisticated. Simply put, we usually see the whole process as:

- Put up $100 of capital
- Borrow $100
- Buy $200 of shares

Suppose the expected return on stocks is 9% a year, and the expected volatility is 15%. This way of leveraging our stock investment will give us an expected return of 18% (less borrowing costs) with a volatility of 30%. Once borrowing costs are factored in, while our absolute returns goes up, our risk does too, and the overall risk-return actually falls a bit. This is almost like a “no pain, no gain” school of investing!

Part of the reason why this seems to be the main way we think about borrowing to invest is because the investment advisory process focuses on the return we can get for the risk we take. For example, we usually start off our journey through investment advisory by answering questions on the amount of risk we are willing to take, or our risk tolerance. Some outcomes of this may be:

- If we have a low risk tolerance, we are then recommended a portfolio which is split 50:50 across stocks and bonds, so perhaps for an expected return of 6.5% (9% for stocks, 4% of bonds) for a volatility of 9%
- Or, if we have a higher risk tolerance (especially for the young), we may be recommended a 100% stock portfolio, for an expected return of 9% and volatility of 15%
- Now, if we are real risk-takers, we may then leverage our all stock portfolio 2X, to get an expected return of close to 18% and volatility of 30%.

But what if we instead see this as being about taking the risk for the return we need? Suppose, instead, we followed our instructions from the post ** How to Invest with Leverage Safely** and constructed a risk-parity portfolio of leveraged bonds and unleveraged stocks which yields a 9% expected return for a risk of 10.6%. This would mean, if we have low risk tolerance (akin to the 50:50 portfolio recommended above), we could scale down our leveraged risk-parity portfolio to achieve the same 6.5% expected return for only 7.7% volatility! In this instance, we are using borrowing to reduce the risk we need to take to achieve a certain level of expected investment returns.

Why do we not think about investments in this manner?

- For a start, it could be because there is a lack of deeper knowledge and understanding about the goals and tools of investment, beyond the simple stocks vs bonds concepts
- Secondly, it could also be because our investment and financial advisors have no interest in doing so. After all, they are usually rewarded either based on Assets Under Management (AUM), or commissions, both of which reward higher risk taking by the client to grow assets more aggressively.

Therefore, the answer to the question of “Should I borrow to invest?” is a qualified “Yes”. ** And the evidence from the past decade supports this**. If leverage is available and at a low rate of interest, then it should be considered during the process of investment portfolio construction, with the aim of reducing the risk needed to attain a certain level of returns.

However, it should not be the case that leverage is used solely to “juice” up returns. If that is the case, it is no better than gambling by taking a larger bet on the portfolio. The opposite if also true, leverage should not be ruled out just because it is considered risky. After all, we have few qualms when it comes to taking out a mortgage loan when purchasing property. And in the case of property financing, borrowing in order to purchase a larger property beyond what we can afford in cash does help reduce the risks we face as well. Risks such as:

- Rental inflation
- The need to move when our family outgrows the size of the home
- Being evicted at the landlord’s whim

#### How much leverage can I take on?

If you have gotten this far, you’ve probably convinced yourself that you should consider taking some leverage to invest. But the million dollar question is: “How much leverage can I take on?”. As with all things, there a few ways to think about this, namely:

- Maximising the amount of leverage the lending institution gives for the type of asset pledged
- Taking on just enough leverage to be able to reduce the risk (for a given level of return) to the level based on risk tolerance
- Minimising the risk of a margin call

Let’s look at each of them in turn!

###### 1. Maximising the amount of leverage the lending institution gives for the type of asset pledged

If we go around shopping for Pledged Asset Lines (PAL) and secured loans in general, we’ll see that different types of assets have different Loan-To-Values (LTV), or the maximum amount the lending institution will lend against the assessed value of the asset. For example:

###### Typical LTV values by Asset Pledged

Asset Pledged | LTV |
---|---|

Residential Property | 70% to 75% |

Commercial Property | Up to 60% |

Bond Fund | 80% |

Equity Fund/ETF | 70% |

Single Premium Insurance Policy | 65% |

Individual Stocks | 50% to 70% |

And the list goes on. But there are also assets, such as mid cap or small cap stocks, which while fast growing, may still be considered speculative, and hence command an LTV of exactly 0%!

Now, since these are the LTVs given by the lending institutions, they should be safe right? And in order to maximise our return on investment, we should maximise our borrowings to the limit given by the LTVs, right? Actually, no! Maximising borrowings up to the LTV for a particular type of asset (with the exception of property) is the fastest way to be hit with a margin call, which can potentially wipe out all your investments!

Imagine if you have maximised your borrowing on an equity ETF to the 70% permissible. The moment the value of the ETF dips, you’d have gone above the maximum LTV, and will need to top up your capital to avoid the investment being force sold. Maximising the LTV will only lead to an endless sequence of margin calls, topping up capital, rinse and repeat. Clearly not the things to be hassled with, especially if you are not a full time investor.

So why are lending institutions seemingly so generous with the LTVs? They are not set for the borrower’s benefit, for a start. Instead, they are set to maximise the benefit to the lender (in terms of how much they can lend and earn interest rom, as well as to encourage trading and commissions), balanced against the need to protect themselves from defaulting investors when the market dips. So, let’s just forget about maximising the borrowing up to the limit of the LTVs for now.

The only exception is for property, where the investor should definitely maximise the borrowing up to the limit of the LTV. Why? Because we do not revalue property by the second or minute, as financial assets are. In fact, they are generally not revalued for a very long time, which means that the chance of a margin call due to a fall in the property value is almost nil. “Almost”, because weaker borrowers have been known to be hit with a capital/deposit call on their mortgages during particularly severe financial crises (think Asia Financial Crisis in 1998). In any case, lending institutions tend to be conservative when assessing the value of the property in the first place, so there is an additional buffer to protect the borrower from a margin call. So, maximise your housing loan if you can!

###### 2. Taking on just enough leverage to be able to reduce the risk to the level based on risk tolerance

As we have mention earlier, we can use borrowing for investment to reduce risk to the level of the investor’s risk tolerance, while still achieving the same level of required return. Let’s use an example to illustrate this:

Suppose an investor requires a return of 6.5% per annum on his/her investments for the next 30 years in order to finance retirement for him and her, plus a bequest for the children. There are a few ways to do this:

- Invest 100% in equities, with a long term expected return of 9% and volatility of 15%
- Invest in a balanced portfolio, split 50:50 between stocks and bonds. The expected return on this portfolio is 6.5% per annum with a volatility of 9%
- Invest in a risk-parity portfolio, split 50:50 between stocks and bonds, with the bond portion leveraged 3X (less than the maximum 5X or 80% LTV). The expected return to this strategy is 9% per annum with a volatility of 10.6%

###### How a Risk-Parity Portfolio Works

Now, further suppose that this investor is fairly conservative, and leans towards the risk of a balanced portfolio. In such a case, Portfolio 1, which is 100% in stocks is out. While the returns look attractive, the volatility is heart-stompingly high for this investor.

Portfolio 2 might fit the bill, as the returns and the risk fit with the return requirements, and risk tolerance of the investor. in most cases, this would be the end of the matter. But can we do better than this?

If the investor has the appetite for a little bit of borrowing, Portfolio 3 might also be a suitable solution. Since the investor only need 6.5% returns per annum, Portfolio 3 can be scaled down by 30% to achieve the desired results of a return of 6.5% per annum, with a volatility of only 7.7%! But how much leverage is exactly needed for this? Now, the original portfolio was split 50:50 between stocks (purchased in cash) and bonds (leveraged 3X), which means that portfolio was constructed with $67 of cash and $33 of borrowing, which implies a leverage of 33%. Now, since we want to scale this down by 30%, the final leverage used is 22%.

At this low level of leverage, plus the liquid nature of the asset portfolio, the risk of a margin call are virtually nil. And this allows the investor to achieve his/her goals with a lower level of volatility risk! This would be a conservative case for the use of leverage in investing.

###### 3. Minimising the risk of a margin call

The typical investor is usually not too concerned about reducing risk while achieving his/her investment goals. Rather, the aim is to achieve higher returns through the use of leverage. But as we have argued earlier, maximising the LTVs which lending institutions give will be the fastest way to achieve these high returns, but is also the fastest way to financial ruin too. How should the typical investor navigate this?

One approach to this is to set the leverage according to the risk of the assets to be pledged. To do so, let’s take a look at how lending institutions set their LTV limits. Remember, the LTV limits are set by lending institutions to ensure they do not get caught out by defaulting investors. So they are based on how quickly they can sell the asset off (in a distressed and falling market) if the investor fails to meet a margin call.

Suppose the price of a stock usually moves up or down by up to 5% a day, i.e. has a daily volatility of 5%. On a really bad day, suppose this can double, i.e. fall by 10%. And over the course of a week, it can fall by 25% (for the stats nerds, volatility scales by the square root of time). Add in some slippage due to the bid-ask spread and taking costs, the lending institution can expect to lose up to 30% on the value of a stock should the investor fail to meet the margin call and defaults. When this happens, the lender will sell off the stock as fast as they can, typically within 5 business days or less. Hence, setting the LTV for a stock at 70% helps to protect the lender from a loss in such an instance.

###### How to calculate LTVs for lending

Computation Step | |
---|---|

1. Daily volatility | 5% |

2. Extreme daily volatility (2 standard deviations) | 10% |

3. Extreme weekly volatility (2.5X) | 25% |

4. Buffer for trading costs | 5% |

5. Total buffer (LTV is 1 – minus buffer) | 30%, or LTV = 70% |

So, if your aim is to avoid getting a margin call, then we need to work out what is a safe level of buffer we require. To continue the example above, if the aim is to avoid a margin call over 6 months (26 weeks), we need to multiply line 3 above, “Extreme weekly volatility” by 5X to estimate the buffer required:

###### Safe LTV for a stock

Computation Step | |
---|---|

A. Extreme weekly volatility | 25% |

B. Extreme half-yearly volatility (5X) | 125% |

C. Total buffer | 125%, or LTV = 0% |

From this, we can see that the safe LTV for a stock to avoid margin calls is 0%! That is to say, it is never safe to borrow to invest in stocks! But what about bonds or bond funds?

Suppose that a bond or bond fund has a daily volatility of 0.75%. How would the safe leverage level be for this bond?

###### Safe LTV for a Bond Fund

Computation Step | |
---|---|

1. Daily Volatility | 1% |

2. Extreme daily volatility (2 standard deviations) | 2% |

3. Extreme weekly volatility (2.5X) | 5% |

4. Extreme half-yearly volatility (5X) | 25% |

5. Total Buffer (LTV is 1 – minus buffer) | 25%, or LTV = 75% |

Hence, if we use leverage in investing, it should be used on bonds or bond funds, although it is still dangerous or risky to go all the way up to 80% LTV. Clearly, somewhere between 3X leverage (67% LTV) or 4X leverage (75% LTV) would be safest.

But very few people invest solely in bonds. Bonds are usually part of a diversified and balanced portfolio with stocks. In such a case, since bonds are far less likely to trigger a margin call, it is far better to borrow against the bonds up to the maximum LTV of 80%, and then pledge the value of the stocks in the portfolio to reduce the overall leverage down to the desired level. For example, in the risk-parity portfolio:

###### Leverage in the Risk-Parity Portfolio

Value of bonds | $100 of which $20 is capital |

Borrowing against bonds | $80 out of $80 allowed |

Value of Stocks | $100 of which $100 is capital |

Borrowing against Stocks | $0 out of $70 allowed |

Total Portfolio Value | $200 |

Total Capital Invested | $120 |

Total Borrowing and Leverage | $80, or LTV of 40% of portfolio |

Clearly, if the mix of bonds in the portfolio were different, the overall LTV of the portfolio will also differ. Which means that the larger amount of low risk assets we have in the portfolio, the higher the LTV will be. A 100% bond portfolio can have an LTV which is close to 80%. A portfolio with fewer bonds will be able to justify a much lower LTV. In short, when we take on leverage with the aim to minimise the chance of a margin call, it is the amount of “safe” assets, like high quality bonds and bond funds, in the portfolio, which determines the optimum leverage.

It is the amount of “safe” assets, like high quality bonds and bond funds, in the portfolio, which determines the optimum leverage

#### Conclusions: How much leverage can I take on?

in this rather long follow up to our earlier post * How to Invest with Leverage Safely*, we address two questions:

- Should I borrow to invest?
- How much leverage can I take on?

While most investment advisory would advise against leveraged investment, for a more sophisticated investor, leverage can be used judiciously to ** reduce**, rather than add, risk. Leverage is just one of many tools in the investors’ toolkit, and can be beneficial when used with care. When it is used bluntly, for example, to get higher returns at higher risk, it becomes a dangerous tool.

But even where leverage is used with care, we need to answer the question of how much leverage to take. Here, we discuss one approach, which is to minimise the risk of a margin call, as a way to do so. The conclusions we reach are that it is the amount of safe assets in the portfolio which ultimately determine the optimal leverage, rather than any fixed benchmark, so as 30% or 35% or even 40%.

Note that building such a leveraged risk-parity portfolio takes quite a bit of effort. But now, ** there is an ETF which allows you to do so quite easily**!

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